Take the function defined by the series $f(t) = 6 + \sum_{n=1}^\infty \frac{3}{n^5} \cos( n \pi t)$.

Find the antiderivative which is in the form $F(t) = Ct + \frac{a_0}{2} + \sum_{n=1}^\infty a_n \cos( n \pi t) + b_n \sin( n \pi t)$, and such that $F(0) = 8$
$C = {}$
$a_0 = {}$
$a_n = {}$
$b_n = {}$

help (formulas)