Vector Calculus · Medium problem

A river's current is modeled by $\mathbf F=(x,y)$ near the point $(\tfrac12,\tfrac12)$. Find the flux $\displaystyle\int_C\mathbf F\cdot\mathbf n\,ds$ of $\mathbf F$ across the straight segment $C$ from $(1,0)$ to $(0,1)$, where $\mathbf n$ is the unit normal pointing away from the origin.