MHB Continuous periodic piecewise differentiable

[Dustinsfl]

Suppose that $f(\theta)$ is a continuous periodic piecewise differentiable function. Prove that $f(\theta) = f(0) + \int_0^{\theta}g(t)dt$ for a piecewise continuous $g$.

I just need a nudge in the right direction here.

 

[tarantella]

Can you do it when $f$ is differentiable? THen use the fact that there are only finite many points where $f$ is not differentiable.