Answer
Use rectangular coordinates and write $\iint_Rf(x,y)dA=\int_{-1}^1\int_0^{1-x^2}f(x,y)dydx$.
Work Step by Step
The region $R$ can be easily written as the set of points in rectangular coordinates, that is $R=\{(x,y)|-1\leq x\leq 1,0\leq y\leq 1-x^2\}$.
We decide to use rectangular coordinates and write $\iint_Rf(x,y)dA=\int_{-1}^1\int_0^{1-x^2}f(x,y)dydx$.
