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))#.
