Vector Calculus · Superchallenge problem

Let $\mathbf F = \left(y + 3x^2,\; 2y\right)$. Among all curves $C$ from $(-1, 0)$ to $(1, 0)$ that have length $\pi$ and lie in the half-plane $y\ge 0$, find the largest possible value of the work $\displaystyle\int_C\mathbf F\cdot d\mathbf r$. Give your answer in terms of $\pi$.