Calculating a Fourier series for a periodic step function

In this video, I calculate the Fourier coefficients for the Fourier series of a periodic function with jumps in it.

[kumuduninilanthi]

why did you put a limit -1/2 to 1/2 instead of 0 to 1? if it is not a step function we just put f(x)=1 or something but how do we put value for f(x) if it was a step function? (for final answer )

[NMelvynN]

what if instead of a -1 the function was actually =0 between 0 and 1/2?? please help

[mysteriousmufman]

You should be changing n to (2m-1) to account for the fact that even integers of n zero it out shouldn't you?

[gilbert]

At around 1:30, you could have integrated from -1/2 to 0, and plugged in +1 for your f(x), correct? Just making sure I understand. Great vid!