Let $0 < a < b$ and let $s\in\mathbb R,$ but $s\not\in\mathbb Z$, then the Riemann integral of the general power function of positive numbers. $$\int_a^bx^s dx=\frac{x^{s+1}}{s+1}\begin{array}{|l}a\\\\b\end{array}.$$
The above formula also holds for the following cases: * $s\in\mathbb N$ and arbitrary $a,b$ with $a < b$, * $s\in\mathbb Z$ with $s\le -2$, and $0\not\in [a,b]$.
For $s=-1$ the above formula is not defined.
Proofs: 1
