The question asks to write a definite integral on the integral [1,5] for the following limit.

$\displaystyle

\mathop {\lim }\limits_{n \to \infty } \sum\limits_{k = 1}^n {\left( {\frac{4}{n} \times \frac{1}{{\left( {2 + \frac{{4k}}{n}} \right)}}} \right)}

$

I understand how to evaluate a Riemann sum on an interval for n strips etc.

But I am at a complete loss on how to work limits into an integral.

In desperate helps for some understanding on these, I've gone through my notes and text several time and cannot understand it.