Each of m and n is a positive integer with m < n. Evaluate this double definite integral in terms of m and n.

∫ ∫ [x+y]*{x+y}*(x+y) dx dy for x = 1 to m and, y = 1 to n

*** [x] denotes the smallest integer ≤ x, and {x} is the decimal part of x, ie {x}=x-[x].