Chapter 5, Problem 2RCC

(a)

To determine

The definition of the definite integral of f from a to b.

(b)

To determine

The geometric interpretation of ${\displaystyle \underset{a}{\overset{b}{\int }}f\left(x\right)dx}$ when $f\left(x\right)$ is positive.

(c)

To determine

The geometric interpretation of ${\displaystyle \underset{a}{\overset{b}{\int }}f\left(x\right)dx}$ when $f\left(x\right)$ takes both positive and negative values.