What's the importance of Reiman's sum ?

The Riemann sum becomes the definition of an integral as you limit your n to approaching infinity. the importance of it is it gives you the area under a curve for any arbitrary curve, i challenge you to find the area under e^x without it.

It's applications are apparent in just about any subject. the Riemann sum makes it possible to calculate continuously compounding interest, it allows you to find velocity from acceleration, or postion from velocity in physics, depending on what you do may change the applications but im sure you wake up to an alarm clock every morning, which required the Riemann sum to create. you may not particularly use the Riemann sum in your daily life but it is always all around you as just about any product you buy was created by some sort of engineers and they use integration, a direct product of the Riemann sum everyday.

you cant get an exact rieman sum unles you express it as the limit of n to infinity where n is the number of subdivisions of any of the three types of riemann sums. I actually had the equation that let me do that, I figured it out a few years back when i got sick when my fam went to disney. But i lost it and i dont feel like finding it again

Riemann. The process gives you the area under a curve, which has thousands of applications in science and industry, even in business. Whose daily life? Scientists? Engineers? Teenagers?

Here it is in Wikipedia

http://en.wikipedia.org/wiki/Riemann_sum