Question about Evaluating Integrals using Limits and Sigmas

OK, I hope this makes sense.

So I am taking my second class in calculus but there has been a three year lapse in the time I have taken the first class so I am a little rusty.

I am trying to create an expression for the area under the curve using limits.

Specifically, the question asks:

Use Definition 2 to find an expression for the area under the graph of *f* as a limit. Do not evaluate the limit.

http://www.churchleadership.com/temp/Problem.png

http://www.churchleadership.com/temp/Definition.png

Based on that I have garnered the following:

http://www.churchleadership.com/temp/Solution.png

However, I am lost as to how to proceed. Any help that can explain this step by step would be greatly appreciated.

Thank you for your time.