Minimize the following term under the given constraint

Question

If $f(x)$ is a real valued continuous and differentiable function in $[0, 1]$ and $\int_{1/3}^{2/3}f(x)dx = 0$ minimize $\frac{\int_{0}^{1}f'(x)^2 dx}{(\int_{0}^{1}f(x)dx)^2}$