Anti-derivatives of the periodic functions

[cbarker1]

Dear Everyone,

I do not know how to begin with the following problem:Suppose that $f$ is $2\pi$-periodic and let $a$ be a fixed real number. Define $F(x)=\int_{a}^{x} f(t)dt$, for all $x$ .
Show that $F$ is $2\pi$-periodic if and only if $\int_{0}^{2\pi}f(t)dt=0$.
Thanks,
Cbarker1

 

[topsquark]

...if and only if $\int_{0}^{2\pi}f(t)dt$.

if and only if \(\displaystyle \int_0^{2 \pi}f(t)~dt\) is what?

-Dan