A doubt

If you got Int(dA) and A=xy, which are variables, how would that integration become in terms of x and y?

>>10
The question remains, how the hell is dA in terms of x and y.
In this case dA=R*dR*dy, A=((R^2)*y)/2 (a circle of A area)
In the case where A=x*y, dA=dx*dy (a square of A area)
But isn't it supposed to be a sum of the partial derivatives?