Answer
\[\int_{0}^{1}{\int_{-\sqrt{y}}^{\sqrt{y}}{f\left( x,y \right)}dxdy}\]
Work Step by Step
\[\begin{align}
& \int_{-1}^{1}{\int_{{{x}^{2}}}^{1}{f\left( x,y \right)}dydx} \\
& \text{Using the graph to switch the order of integration} \\
& -\sqrt{y}\le x\le \sqrt{y} \\
& 0\le y\le 1 \\
& \text{Then} \\
& \int_{0}^{1}{\int_{-\sqrt{y}}^{\sqrt{y}}{f\left( x,y \right)}dxdy} \\
\end{align}\]
