Integral of Power/Conventional Proof

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

Proof
From the Fundamental Theorem of Calculus, we have:


 * $\displaystyle \frac{\mathrm d}{\mathrm d x}\left({\int f \left({x}\right) \mathrm d x}\right) = f \left({x}\right)$

So:

Integration between the limits gives: