Can someone help me with these two Fourier Series problems please? Also, can you explain how you did the problems because I dont understand how to do Fourier Series :( ...Thanks in advance! :)

#1 Use the Fourier Series

f(x) = {0, -pi < x < 0; x^2, 0 < x < pi

to show that

1 - 1/4 + 1/9 - 1/16 +.... = (pi^2)/12

#2 Establish the result in the problem below, where m and n are positive integers. (Hint: sinA sinB = (1/2) [cos(A-B) - cos(A+B)].)

L

∫ sin((n pi x)/L) sin((m pi x)/L) dx = {0, m≠n; L, m=n

-L