How do I go about this?

I need details solution to study

find any given rectangle ∆ R=(xbase0,xbase0+w).(ybase0.ybase0+h) if we define function A A(R)=
∫ ∫R e^(2iπ(x+y)dxdy

Assuming the range for (x,y) are for all real positive integer ....where do we go from there?

what are the range of x,y. All real positive numbers?