∫ of (x^2) from 0 to 2 proof w/o using fundamental therom, but w/ Riemann Sums

[LearninDaMath]

Homework Statement

\int_0^2 x^2 \, dx using true definition involving Riemann Sums (w/o fundamental theorem).

Homework Equations

I don't know what the relevant equations may be, perhaps some type of lim\sum f(x)(x_{j}-x_{j-1})

The Attempt at a Solution

No attempt. Just seeking the long proof for it. Would be grateful for any and all clues to where I could find the long solution to this.

 

[LCKurtz]

Look at example 2 here for a similar, but different, example:

http://faculty.eicc.edu/bwood/math150supnotes/supplemental21.html

 

[LearninDaMath]

ah thanks, LC, I put that straight to my favorites. I believe that's all I would need to get the concept I'm looking to understand a little better. Appreciate your info.