Answer
$6$
Work Step by Step
Apply RIEMANN SUM:
$\Sigma_{k=1}^n f(c_k) \triangle x=\Sigma_{k=1}^n (\dfrac{8k}{n^2}+\dfrac{2}{n})$
or, $\Sigma_{k=1}^n (\dfrac{8k}{n^2}+\dfrac{2}{n})=\dfrac{8k}{n^2}\Sigma_{k=1}^n (k+\dfrac{2}{n}) $
where $\triangle x=\dfrac{b-a}{n}$ and $c_k=a+\dfrac{k(b-a)}{n}$
Now, $\lim\limits_{n \to \infty} \Sigma_{k=1}^n f(c_k) \triangle x=\lim\limits_{n \to \infty}\dfrac{4(n+1)}{n}+2$
This implies that $\lim\limits_{n \to \infty}6+\dfrac{4}{n}=6$
