6. Prove that the function $f(x) = 3x^2$ is Riemann integrable over the interval $[0, 1]$ and compute
$$\int_0^1 3x^2 dx$$
as the limit of upper (and lower) sums.
[Hint: Consider the uniform partition $P_n$ of $[0, 1]$, given by
$$0 < \frac{1}{n} < \frac{2}{n} < ... < \frac{n-1}{n} < 1$$
and recall that
$$\sum_{k=1}^n k^2 = \frac{1}{6}n(n+1)(2n+1).$$]