The value of the limit $$\lim_{n\rightarrow\infty}\sum_{i=1}^{n} \frac{4}{n} \sqrt{5 + \frac{4 i}{n}}$$ is equal to the area below the graph of a function $f(x)$ on an interval $[A,B]$. Find $f$, $A$, and $B$. (Do not evaluate the limit.)

$f(x)$ =

$A$ = (use $A=0$)

$B$ =