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.
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[Hint: Consider the uniform partition $P_n$ of $[0, 1]$, given by
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$0 < \frac{1}{n} < \frac{2}{n} < ... < \frac{n - 1}{n} < 1$
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and recall that
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$\sum_{k=1}^n k^2 = \frac{1}{6}n(n + 1)(2n + 1).$ ]
[10 Marks]
