Evaluate the Integral

∫∫(x-y)sin(x+y)dxdyover the tilted square region with corners at (0,0)(π/2, π/2)(π,0)(π/2,-π/2) by doing a change of variables u=x+y and v=x-y

I"m having problems calculating the bounds. I think that I need to rewrite the bounds y=x, y=-x, y=-x+π, y=x-π in terms of u and v but I'm having trouble with how to do it. The rest of the problem makes sense to me, just the bounds are giving me some confusion.