Answer
$f(x_{1})\triangle x_{1}+f(x_{2})\triangle x_{2}+f(x_{3})\triangle x_{3}+f(x_{4})\triangle x_{4}+\cdots+f(x_{n})\triangle x_{n}$
Work Step by Step
We expand the sigma notation by writing $f(x_{i})\triangle x_{i}$ as $i$ increases from 1 to n:
$\displaystyle \sum_{i=1}^{n}f(x_{i})\triangle x_{i}=f(x_{1})\triangle x_{1}+f(x_{2})\triangle x_{2}+f(x_{3})\triangle x_{3}+f(x_{4})\triangle x_{4}+\cdots+f(x_{n})\triangle x_{n}$
