imilar to the last problem, our goal for this problem is to compute $\frac{d}{dx}[{\displaystyle \underset{4}{\overset{x^5}{}}}sin(t^2)dt].$

L$)$ Let $G(t)$ be an antiderivative of $sin(t^2),$ i$.$e$.,G^{\text{'}}(t)=sin(t^2).$ Write ${\displaystyle \underset{4}{\overset{x^5}{}}}sin(t^2)dt$ in terms of the funciton $G(t).($Use the First Fundamental Theorem of Calculus.$)$

${\displaystyle \underset{4}{\overset{x^5}{}}}sin(t^2)dt=G|,|-G$

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b$)$ Use part $($a$)$ and the chain rule to find $\frac{d}{dx}[{\displaystyle \underset{4}{\overset{x^5}{}}}sin(t^2)dt].$

$\frac{d}{dx}[{\displaystyle \underset{4}{\overset{x^5}{}}}sin(t^2)dt]=$

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