Chapter 6, Problem 6CRQ

(a)

To determine

To fill: “The fundamental theorem of calculus states that if $f$ is continuous on $\left[a,b\right]$, then ${\displaystyle {\int }_a^{b}f\left(x\right)}dx=$________ , where F is a/an _______ of $f$”.

(b)

To determine

To fill: “The net change in a function $f$ over an interval $\left[a,b\right]$ is given by $f\left(b\right)-f\left(a\right)=$_________, provided that $f$ is continuous on $\left[a,b\right]$”.