Finding the limits for triple integrating a volume

Question

If i want to integrate over the the region $R$ such that $R:={(x,y,z):z\geq x^2+y^2,z \geq 2-2x, z\leq 10 -2y}$, what will the limits be for $x, y$, more importantly how should I systematically think to find the limits for my integrals? Could someone please help me? Is it correct if my integration limits are as such: $\int^{1}_{0} \int^{1}_{0} \int^{10-2y}_{2-2x} dzdxdy$?