Fourier Series Expansion of a Periodic Function f(x)= -k for -π to 0, and k for 0 to π.

Fourier Series Expansion of a step function.
In this video, I have sketched a periodic function:
f(x) = -k for -π to 0
f(x)= k for 0 to π, with f(x+2π) = f(x).
Then obtained its Fourier series representation, and deduced on expression too.