9.1.31 Double integrals

Problem: Change the order of integration: \[ I=\int_{0}^{a} d y \int_{\frac{y^{2}}{2 a}}^{a-\sqrt{a^{2}-y^{2}}} f d x+\int_{0}^{a} d y \int_{a+\sqrt{a^{2}-y^{2}}}^{2 a} f d x+\int_{0}^{2 a} d y \int_{\frac{y^{2}}{2 a}}^{2 a} f d x . \]