Integral of Power

Theorem

 * $\displaystyle \forall n \in \R_{\ne -1}: \int_0^b x^n \mathrm d x = \frac {b^{n+1}} {n+1}$

Fermat's Proof
This proof is is valid only for positive rational numbers, that is, it proves that:
 * $\displaystyle \forall n \in \Q_{>0} : \int_0^b x^n \mathrm d x = \frac {b^{n+1}} {n+1}$