diff --git a/skimage/transform/integral.py b/skimage/transform/integral.py
index 3503a652..fd9f8725 100644
--- a/skimage/transform/integral.py
+++ b/skimage/transform/integral.py
@@ -1,7 +1,8 @@
 import numpy as np
+import collections
 
 
-def integral_image(x):
+def integral_image(img):
     """Integral image / summed area table.
 
     The integral image contains the sum of all elements above and to the
@@ -13,13 +14,13 @@ def integral_image(x):
 
     Parameters
     ----------
-    x : ndarray
+    img : ndarray
         Input image.
 
     Returns
     -------
     S : ndarray
-        Integral image / summed area table.
+        Integral image/summed area table of same shape as input image.
 
     References
     ----------
@@ -27,44 +28,117 @@ def integral_image(x):
            ACM SIGGRAPH Computer Graphics, vol. 18, 1984, pp. 207-212.
 
     """
-    return x.cumsum(1).cumsum(0)
+    S = img
+    for i in range(img.ndim):
+        S = S.cumsum(axis=i)
+    return S
 
 
-def integrate(ii, r0, c0, r1, c1):
+def integrate(ii, start, end, *args):
     """Use an integral image to integrate over a given window.
 
     Parameters
     ----------
     ii : ndarray
         Integral image.
-    r0, c0 : int or ndarray
-        Top-left corner(s) of block to be summed.
-    r1, c1 : int or ndarray
-        Bottom-right corner(s) of block to be summed.
+    start : List of tuples, each tuple of length equal to dimension of `ii`
+        Coordinates of top left corner of window(s).
+        Each tuple in the list contains the starting row, col, ... index
+        i.e `[(row_win1, col_win1, ...), (row_win2, col_win2,...), ...]`.
+    end : List of tuples, each tuple of length equal to dimension of `ii`
+        Coordinates of bottom right corner of window(s).
+        Each tuple in the list containing the end row, col, ... index i.e
+        `[(row_win1, col_win1, ...), (row_win2, col_win2, ...), ...]`.
+    args: optional
+        For backward compatibility with versions prior to 0.11.
+        The earlier function signature was `integrate(ii, r0, c0, r1, c1)`,
+        where `r0`, `c0` are int(lists) specifying start coordinates
+        of window(s) to be integrated and `r1`, `c1` the end coordinates.
 
     Returns
     -------
     S : scalar or ndarray
         Integral (sum) over the given window(s).
 
+
+    Examples
+    --------
+    >>> arr = np.ones((5, 6), dtype=np.float)
+    >>> ii = integral_image(arr)
+    >>> integrate(ii, [(1, 0)], [(1, 2)])  # sum from (1,0) -> (1,2)
+    array([ 3.])
+    >>> integrate(ii, [(3, 3)], [(4, 5)])  # sum form (3,3) -> (4,5)
+    array([ 6.])
+    >>> integrate(ii, [(1, 0), (3, 3)], [(1, 2), (4, 5)])  # sum from (1,0) -> (1,2) and (3,3) -> (4,5)
+    array([ 3.,  6.])
     """
-    if np.isscalar(r0):
-        r0, c0, r1, c1 = [np.asarray([x]) for x in (r0, c0, r1, c1)]
+    rows = 1
+    # handle input from new input format
+    if len(args) == 0:
+        if isinstance(start, collections.Iterable):
+            rows = len(start)
+        start = np.array(start)
+        end = np.array(end)
+    # handle deprecated input format
+    else:
+        if isinstance(start, collections.Iterable):
+            rows = len(start)
+        args = (start, end) + args
+        start = np.array(args[:int(len(args)/2)]).T
+        end = np.array(args[int(len(args)/2):]).T
 
-    S = np.zeros(r0.shape, ii.dtype)
+    total_shape = ii.shape
+    total_shape = np.tile(total_shape, [rows, 1])
 
-    S += ii[r1, c1]
+    # convert negative indices into equivalent positive indices
+    start_negatives = start < 0
+    end_negatives = end < 0
+    start = (start + total_shape) * start_negatives + \
+             start * ~(start_negatives)
+    end = (end + total_shape) * end_negatives + \
+           end * ~(end_negatives)
 
-    good = (r0 >= 1) & (c0 >= 1)
-    S[good] += ii[r0[good] - 1, c0[good] - 1]
+    if np.any((end - start) < 0):
+        raise IndexError('end coordinates must be greater or equal to start')
 
-    good = r0 >= 1
-    S[good] -= ii[r0[good] - 1, c1[good]]
+    # bit_perm is the total number of terms in the expression
+    # of S. For example, in the case of a 4x4 2D image
+    # sum of image from (1,1) to (2,2) is given by
+    # S = + ii[2, 2]
+    #     - ii[0, 2] - ii[2, 0]
+    #     + ii[0, 0]
+    # The total terms = 4 = 2 ** 2(dims)
 
-    good = c0 >= 1
-    S[good] -= ii[r1[good], c0[good] - 1]
+    S = np.zeros(rows)
+    bit_perm = 2 ** ii.ndim
+    width = len(bin(bit_perm - 1)[2:])
 
-    if S.size == 1:
-        return np.asscalar(S)
+    # Sum of a (hyper)cube, from an integral image is computed using
+    # values at the corners of the cube. The corners of cube are
+    # selected using binary numbers as described in the following example.
+    # In a 3D cube there are 8 corners. The corners are selected using
+    # binary numbers 000 to 111. Each number is called a permutation, where
+    # perm(000) means, select end corner where none of the coordinates
+    # is replaced, i.e ii[end_row, end_col, end_depth]. Similarly, perm(001)
+    # means replace last coordinate by start - 1, i.e
+    # ii[end_row, end_col, start_depth - 1], and so on.
+    # Sign of even permutations is positive, while those of odd is negative.
+    # If 'start_coord - 1' is -ve it is labeled bad and not considered in
+    # the final sum.
 
+    for i in range(bit_perm):  # for all permutations
+        # boolean permutation array eg [True, False] for '10'
+        binary = bin(i)[2:].zfill(width)
+        bool_mask = [bit == '1' for bit in binary]
+
+        sign = (-1)**sum(bool_mask)  # determine sign of permutation
+
+        bad = [np.any(((start[r] - 1) * bool_mask) < 0)
+               for r in range(rows)]  # find out bad start rows
+
+        corner_points = (end * (np.invert(bool_mask))) + \
+                         ((start - 1) * bool_mask)  # find corner for each row
+
+        S += [sign * ii[tuple(corner_points[r])] if(not bad[r]) else 0
+              for r in range(rows)]  # add only good rows
     return S
diff --git a/skimage/transform/tests/test_integral.py b/skimage/transform/tests/test_integral.py
index eb92a40b..e05ed397 100644
--- a/skimage/transform/tests/test_integral.py
+++ b/skimage/transform/tests/test_integral.py
@@ -17,15 +17,16 @@ def test_validity():
 
 
 def test_basic():
-    assert_equal(x[12:24, 10:20].sum(), integrate(s, 12, 10, 23, 19))
-    assert_equal(x[:20, :20].sum(), integrate(s, 0, 0, 19, 19))
-    assert_equal(x[:20, 10:20].sum(), integrate(s, 0, 10, 19, 19))
-    assert_equal(x[10:20, :20].sum(), integrate(s, 10, 0, 19, 19))
+    assert_equal(x[12:24, 10:20].sum(), integrate(s, (12, 10), (23, 19)))
+    assert_equal(x[:20, :20].sum(), integrate(s, (0, 0), (19, 19)))
+    assert_equal(x[:20, 10:20].sum(), integrate(s, (0, 10), (19, 19)))
+    assert_equal(x[10:20, :20].sum(), integrate(s, (10, 0), (19, 19)))
 
 
 def test_single():
-    assert_equal(x[0, 0], integrate(s, 0, 0, 0, 0))
-    assert_equal(x[10, 10], integrate(s, 10, 10, 10, 10))
+    assert_equal(x[0, 0], integrate(s, (0, 0), (0, 0)))
+    assert_equal(x[10, 10], integrate(s, (10, 10), (10, 10)))
+
 
 def test_vectorized_integrate():
     r0 = np.array([12, 0, 0, 10, 0, 10, 30])
@@ -40,7 +41,10 @@ def test_vectorized_integrate():
                          x[0,0],
                          x[10, 10],
                          x[30:, 31:].sum()])
-    assert_equal(expected, integrate(s, r0, c0, r1, c1))
+    start_pts = [(r0[i], c0[i]) for i in range(len(r0))]
+    end_pts = [(r1[i], c1[i]) for i in range(len(r0))]
+    assert_equal(expected, integrate(s, r0, c0, r1, c1))  # test deprecated
+    assert_equal(expected, integrate(s, start_pts, end_pts))
 
 
 if __name__ == '__main__':