Chapter 5.6, Problem 1QCE

(a) If $F\left(x\right)$ is an antiderivative for $f\left(x\right)$ , then

${\displaystyle {\int }_a^{b}f\left(x\right)dx}=\text{\_\_\_\_\_\_}$

(b) ${\displaystyle {\int }_a^b{F}^{\prime }\left(x\right)dx}=\text{\_\_\_\_\_\_}$

(c) $\frac{d}{dx}\left[{\displaystyle {\int }_a^{x}f\left(t\right)dt}\right]=\text{\_\_\_\_\_\_\_}$