Chapter 5, Problem 25RE

The definite integral of $f$ over the interval $\left[a,b\right]$ is defined as the limit

${\displaystyle {\int }_a^{b}f\left(x\right)dx}=\underset{\max \Delta x_k\to 0}{\lim }{\displaystyle \underset{k=1}{\overset{n}{\sum }}f\left(x_k^{*}\right)\Delta x_k}$

Explain what the various symbols on the right side of this equation mean.