Express the limit below as a definite integral. The n points $x_0 < x_1 < x_2 < x_3 < \dots < x_n$ evenly divide the interval $[a, b]$ into n subintervals, each of width $w = \frac{b - a}{n}$. Do not evaluate the definite integral.\\
$\lim_{n \to \infty} w \left( \frac{x_0^2}{6} + \frac{x_1^2}{6} + \frac{x_2^2}{6} + \dots + \frac{x_{n-1}^2}{6} \right)$, where $a = 1$, $b = 3$.
