$\int_0^x f(t) dt = \sum_{n=0}^{\infty} \frac{x^{2n+2}}{(2n+2)!}$

$\int_0^x f(t) dt = \sum_{n=0}^{\infty} \frac{x^{2n+2}}{(2n+1)!(2n+2)}$

$\int_0^x f(t) dt = \sum_{n=1}^{\infty} \frac{x^{2n}}{(2n)!}$

$\int_0^x f(t) dt = 1 - \cosh(x)$