Answer
\[\int_{0}^{1}{\int_{{{x}^{2}}}^{\sqrt{x}}{f\left( x,y \right)}dydx}\]
Work Step by Step
\[\begin{align}
& \int_{0}^{1}{\int_{{{y}^{2}}}^{\sqrt{y}}{f\left( x,y \right)}dxdy} \\
& x={{y}^{2}}\to y=\sqrt{x} \\
& x=\sqrt{y}\to y={{x}^{2}} \\
& \text{Change the order of integration using the graph shown below} \\
& \int_{0}^{1}{\int_{{{y}^{2}}}^{\sqrt{y}}{f\left( x,y \right)}dxdy}=\int_{0}^{1}{\int_{{{x}^{2}}}^{\sqrt{x}}{f\left( x,y \right)}dydx} \\
\end{align}\]
