Determine value of the integration Determine value of the integration $$I=\iint_{D} \sqrt{\left|y-x^2\right|} \, dx \, dy$$ with $$D=[-1,\: 1]\times [0,\: 2]$$
My tried:
$$I=2 \int_0^1 \left(\int_{x}^{2}\sqrt{y-x^2} \, dy\right) \, dx+I_1$$
Find $I_1$.

An idea: the wanted integral seems to be
$$2\int\limits_0^1\int\limits_\sqrt x^1\sqrt{x^2-y}\,dydx+2\int\limits_0^1\int\limits_0^\sqrt x\sqrt{y-x^2}\,dydx+2\int\limits_0^1\int\limits_1^2\sqrt{y-x^2}\,dxdy$$
