Chapter 5, Problem 47RE

Define $F\left(x\right)$ by

$F\left(x\right)={\displaystyle {\int }_1^x\left(t^3+1\right)dt}$

(a) Use part $2$ for the Fundamental Theorem of Calculus to find $F^{\prime }\left(x\right)$ .

(b) Check the result in part (a) by first integrating and then differentiating.