The parabolas $\displaystyle x = -y^2, x = 2y - y^2, x = 2 - y^2 - 2y$ divide the plane into 7 regions, of which only one is bounded. Let this region be A. Find a change of variables such that the first two parabolas become u=0 and v=0. Evaluate the double integral $\displaystyle \int_{A} x dx dy$.