Chapter 5 - Section 5.3 - The Fundamental Theorem of Calculus - 5.3 Exercises - Page 406: 8

$g'(x)=2+\sin x$ See image for graph of $g(x)$

a) $\frac{d}{dx}\int_0^x(2+\sin t)dt=2+\sin x$ b) $\int_0^x(2+\sin t)dt=F(x)-F(0)=2x-\cos x-2\times0+\cos0=2x-cosx+1$ $\frac{d}{dx}(2x-cosx+1)=2+\sin x$ See image for graph of $g(x)$