Let $D$ be the region in the first quadrant of the $xy$-plane, bounded by tge curves $y=x^2$, $y=x^2+1$, $x+y=1$, and $x+y=2$. Using an appropriate change of variables, compute the integral $\int \int_D x \sin (y-x^2) dA$.
Would $u=y-x^2$ and $v=x+y$ be a good change of variables? I am not very good at coming up with good changes of variables. Also, can Green's Theorem somehow be applied here?