Given $R_n = \frac{1}{n} \sum_{i=1}^{n} \left[ 4 \left( 6 + i \frac{1}{n} \right)^4 - 3 \left( 6 + i \frac{1}{n} \right)^3 \right]$, express the limit as $n \to \infty$ as a definite integral, that is provide $a$, $b$ and $f(x)$ in the expression $\int_a^b f(x) dx$.
$a = \text{_____}$, $b = \text{_____}$, $f(x) = \text{_____}$
