I am studying for a calculus class(using Stewart) and this question came up in a list of exercises (from my university):
Question $\rightarrow$ Find $\int_{a}^{b}e^xdx$
I reached $$\lim_{n\to\infty}\frac{(b-a)e^a}{n}\sum_{i=1}^{n}e^{\frac{(b-a)i}{n}}$$
and I should be able to solve it if I knew $\sum_{i=1}^{n}e^n$. The resolution of the list of exercises only brushes it off by making $$\sum_{i=1}^{n}e^{\frac{(b-a)i}{n}}=\frac{e^{\frac{(b-a)}{n}}(e^{\left(\frac{b-a}{n}\right)n}-1)}{e^{\left(\frac{b-a}{n}\right)}-1}$$
How can you prove this?