Double integral over a slanted parallelogram

Let $S\subseteq\mathbb{R}^{2}$ be the region bounded by the parallelogram with vertices at the points $(1,0)$, $(3,2)$, $(3,5)$ and $(1,3)$. Then, the value of the integral $\displaystyle\iint_{S}(x+2y)\,dx\,dy$ is equal to __________.