Vector Calculus · Hard problem

Let $C$ be the arc of the parabola $y = 1 - x^2$ above the $x$-axis, from $(-1, 0)$ to $(1, 0)$, and let $\mathbf n$ be its unit normal pointing to the upper (convex) side, away from the origin. Find the flux $\displaystyle\int_C\mathbf F\cdot\mathbf n\,ds$ of $\mathbf F = (x,\; y)$ across $C$.