Answer
\[\int_{0}^{1}{\int_{y-1}^{1}{xy}dxdy}\]
Work Step by Step
\[\begin{align}
& R=\left\{ \left( x,y \right):y-1\le x\le 1,\text{ 0}\le y\le 1 \right\} \\
& \text{It is preferable that the outer limits of integration are constant} \\
& \text{, then} \\
& \iint\limits_{R}{f\left( x,y \right)}dA=\int_{0}^{1}{\int_{y-1}^{1}{xy}dxdy} \\
\end{align}\]
