Introduction to Limits · Superchallenge problem

Express the area under $y=3x^{2}+1$ over $[0,2]$ as a right-endpoint Riemann sum with $x_{k}=\dfrac{2k}{n}$ and $\Delta x=\dfrac{2}{n}$, then evaluate

using $\displaystyle\sum_{k=1}^{n}k^{2}=\frac{n(n+1)(2n+1)}{6}$.