$f(x)=\int_{0}^x \cos^4 t\, dt$=?

$f(x)=\int_{0}^x \cos^4 t\, dt$=?

How to prove that if $f(x)=\int_{0}^x \cos^4 t\, dt$ then $f(x+\pi)$
equals to $f(x)+f(\pi)$
I thought to first integrate $\cos^4 t$ but this might be the problem of
Definite Integral