Answer
Use rectangular coordinates and write $\iint_R f(x,y)dA=\int_{-1}^1\int_0^{\frac{x+1}{2}}f(x,y)dydx$.
Work Step by Step
The region $R$ in the Figure is bounded by the lines $y=\frac{x+1}{2}$, $y=0$, $x=-1$, and $x=1$.
Then, we decide to use rectangular coordinates, that is $R=\{(x,y)|-1\leq x\leq 1,0\leq y\leq \frac{x+1}{2}\}$ and the integral can be expressed as $\iint_R f(x,y)dA=\int_{-1}^1\int_0^{\frac{x+1}{2}}f(x,y)dydx$.
