z= 0 is the xy-plane, z= 2y is a plane at an angle above the xy-plane. \(\displaystyle y= x^2\) and y= x are perpendicular to the xy-plane.
y= x^2 is a parabola and y= x is a line that intersects that parabola at (0, 0) and at (1, 1). To find the area of the figure bounded by them you would integrate \(\displaystyle \int_0^1\int_{x^2}^x dydx\). To find the volume of the region above that area, do \(\displaystyle \int_0^2\int_{x^2}^x 2y dydx\).