Let $f(x)=cos(x^2)$ and $g(x)=cos(x^3).$ For each of the following pairs of integrals, explain which one has a greater value.

$($a$){\displaystyle \underset{0}{\overset{1}{}}}f(x)dx$ and ${\displaystyle \underset{0}{\overset{1}{}}}g(x)dx$

$($b$){\displaystyle \underset{0}{\overset{1}{}}}f(x)dx$ and ${\displaystyle \underset{cos1}{\overset{1}{}}}{f}^{-1}(x)dx$

$($Note that $f$ has an inverse defined on $cos1,1$ because $f$:$[0,1][cos1,1]$ is strictly decreasing.$)$