This is a definite double integral, over the square
R: a<=x<=b and a<=y<=b.
The order of integration can be changed, either way.
Also, int f(y)dy, from y=a to y=b =.int f(x)dx, from x=a to x=b .
The given double integral
=int x dx int df(y) -int dx inty df(y), over x in[a,b] and yin[a, b]
=[(b^2-a^2)/2][f(b)-f(a)]-(b-a){[yf(y)], between y=a and y=b}+(b-a)int
f(y) dy, over a<=y<=b#
= (b^2-a^2)/2(f(b)-f(a))-(b-a)(bf(b)-af(a))
+(b-a) intf(x) dx, between x=a and x=b
=(b-a) int f(x) dx, between x=a and x=b, -((b-a)^2/2)(f(a)+f(b)).
