Answer
\[\int_{0}^{1}{\int_{y}^{2-y}{f\left( x,y \right)dx}dy}\]
Work Step by Step
\[\begin{align}
& y=-x+2\Rightarrow x=-y+2 \\
& \text{From the graph, the region }R\text{ is} \\
& R=\left\{ \left( x,y \right):y\le x\le -y+2,\text{ 0}\le y\le 1\text{ } \right\} \\
& \text{Then,} \\
& \int_{0}^{1}{\int_{y}^{2-y}{f\left( x,y \right)dx}dy} \\
\end{align}\]
