Lebesgue integral: Does the following integral exists

Question

I'm new to integration theory. The question is:

'Does the following integral (with respect to the 2-dimensional Lebesgue measure) exists? $$\int_{[0,1]\times[0,1]}\frac{x-y}{(x+y)^2}d\lambda^2(x,y)$$'

I don't know how to begin with this one. I use the book 'Measures, Integrals and Martingales'

Answer 1

Make the change of variables $v=x-y,u=x+y$ to see that the integral does not exist.