Definite Integral & Limit: Proving a Relation

[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.)