Help with Piecewise function

[salvomic]

yes, I'm skeptical also of our beloved Prime

My function has a discontinuity in 0 (and also in -π and π) and is a periodic one.
Analyzing it with Fourier analysis I should have bk = int(f(t)*cos(k*t),x,-pi,pi) -> 0 if even, 4/(k*pi) is odd.
With the above assumptions in Prime I get 0 (after the right warning about integration: "Piecewise definite integration: can only handle linear < or > condition")...

Ok, I'm asking too to Prime

Greetings