Haberman 3.5 - Term-by-term integration of Fourier series

0:00 - Introduction
1:52 - Main theorem
14:50 - Integrating the sine series of 1
22:11 - Integrating the cosine series of x
28:26 - Proof of the main theorem
36:02 - Proof, computing Fourier coefficients
46:13 - Proof, computing the constant term and final bits

[devanshiagnihotri]

Is there any condition for f(x) ? Like we have in differentiation