Chapter 6.4, Problem 215E

In the following exercises, find the Maclaurin series of $F(x)={\displaystyle \underset{0}{\overset{x}{\int }}f(t)dt}$by integrating the Maclaurin series of f term b term. If f is not strictly defined at zero, you may substitute the value of the Maclaurin series at zero.

215. $F(x)={\displaystyle \underset{0}{\overset{x}{\int }}\cos (\sqrt{t})dt;}$ $f(t)={\displaystyle \underset{n=0}{\overset{\infty }{\sum }}{(-1)}^n\frac{x^n}{(2n)!}}$