Proof regarding the primitives of periodic functions

Question

Let $ f:R \to R $ be an integrable, periodic function. Prove that any primitive of such a function can be written as a sum of a periodic function and a function of the form $G(x)=ax$ where $a$ is a real constant. The text sounds rather ambiguous to me and I can't find a decent starting point for a proof..Any ideas ?

Answer 1

Let $f(x)=P(x)+k$ where $P(x)$ is a periodic function, $k$ is constant, you have to prove that $\int f(x)dx=P_2(x)+kx$ where $P_2(x)$ must be periodic function(prove that) and $kx$ is your $G(x)=ax$.