$(3$ pts$)14$a$)$ Recall that the MacLaurin Series for $f(x)=cosx$ is ${\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^n}{(2n)!}{x}^{2n}.$ Use this MacLaurin Series to find the MacLaurin series for $f(x)=cos(x^2).$

$(3$ pts$)14$b$)$ Use your infinite series from part $($a$)$ to find the first three $($nonzero$)$ terms of the antiderivative for ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}cos(x^2)dx$

$)14$c$)$ Use your anti$-$derivative from part $($b$)$ to approximate the value of the definite integral