Show that a limit of a sum is a definite integral

[dtl42]

Homework Statement

Show that each limit is a definite integral.
$$Lim (n \rightarrow \infty)$$ of $$\sum \frac{n}{n^{2}+i^{2}}$$ from $$i=1$$ to $$n$$

Homework Equations

$$Lim (n \rightarrow \infty)$$ of $$\sum f(c)\Delta X$$ from $$i=1$$ to $$n$$

The Attempt at a Solution

I can't really get this started, so any help at all would be great.

Thanks.

 

[foxjwill]

Try multiplying by $$\frac{\frac{1}{n^2}}{\frac{1}{n^2}}$$.

 

[HallsofIvy]

What do you think $\Delta x$ should be?

(My hint is really the same as foxjwill's.)