Riemann zeta function and Bernoulli function

Question

I encountered the following problem:

Show that $$\zeta(2n+1)=\frac{(-1)^{n+1}(2\pi)^{2n+1}}{2(2n+1)!}\int_0^{1}B_{2n+1}(x)\cot({\pi}x)dx$$

where $B_{2n+1}(x)$ is the Bernoulli polynomial.

This problem can be found here.