Chapter 4.3, Problem 6E

Sketch the area represented by $g\left(x\right)$. Then find $g\prime \left(x\right)$ in two ways: (a) by using Part 1 of the Fundamental Theorem and (b) by evaluating the integral using Part 2 and then differentiating.

$g\left(x\right)={\displaystyle {\int }_0^x\left(2+\sin t\right)}dt$