Here's a movie!

First, we see a Fourier approximation to the function in Problem 12, which is 0 from -π to 0 and x^2 from 0 to π.
Each frame adds another term of the form (a_n)cos(nx) or (b_n)sin(nx) to the sum, ending with n = 21.
Next, we see the same process for the function Problem 14, which is (x+π) from -π to 0 and x from 0 to π.
There are fewer nonzero terms in this sum, so we go up to n = 42.