Math Physics:Parseval's Theorem

$\int_{-L}^{L} \left| f(x) \right|^2 \, dx = \int_{-L}^{L} f(x)^* f(x) \, dx$

$\int_{-L}^{L} \left[ \frac{a_0}{2} + \sum_{n=1}^{\infty} \left( a_n \cos \frac{n \pi x}{L} + b_n \sin \frac{n \pi x}{L} \right) \right] \left[ \frac{a_0}{2} + \sum_{m=1}^{\infty} \left( a_m \cos \frac{m \pi x}{L} + b_m \sin \frac{m \pi x}{L} \right) \right]\, dx$

$\int_{-L}^{L} \left( \frac{a_0}{2} \right)^2 \, dx + \frac{a_0}{2} \sum_{m=1}^{\infty} \int_{-L}^{L} \cos \frac{m \pi x}{L} + \sum_{n=1}^{\infty} \sum_{n=1}^{\infty} \left[ a_n a_m \int_{-L}^{L} \cos \frac{n \pi x}{L} \cos \frac{m \pi x}{L} + b_n b_m \sin \frac{n \pi x}{L} \sin \frac{m \pi x}{L} \right]$

not done!