Integral of Power/Conventional Proof

Proof
From the Fundamental Theorem of Calculus:


 * $(1): \quad \ds \int_0^b x^n \rd x = \bigintlimits {\map F x} 0 b = \map F b - \map F 0$

where $\map F x$ is a primitive of $x^n$.

By Primitive of Power, $\dfrac {x^{n + 1} } {n + 1}$ is a primitive of $x^n$.

Then: