$(3$ points$)$ Approximate the following integral using power series. The error should be less than $0\mathrm{.}0001.$ Hint: integrate the series for $cos(x^2)$ and remember that the term immediately after the last one added must have magnitude less than the desired error. Substitute $x^2$ into the series for $cos(x)$ first. The number of terms needed is not large.

${\displaystyle \underset{0}{\overset{\frac{1}{2}}{}}}cos(x^2)dx$