The following sum $$\sqrt{6 + \frac{2}{n}} \cdot \left( \frac{2}{n}\right) + \sqrt{6 + \frac{4}{n}} \cdot \left( \frac{2}{n}\right) + \ldots + \sqrt{6 + \frac{2 n}{n}} \cdot \left( \frac{2}{n}\right)$$ is a right Riemann sum for the definite integral $$\int_{3}^b f(x)\, dx$$
where $b$ =
and $f(x)$ =

It is also a Riemann sum for the definite integral $$\int_{6}^c g(x)\, dx$$
where $c$ =
and $g(x)$ =

The limit of these Riemann sums as $n \to \infty$ is