I took up to business calculus in math..........a watered down version of calculus..........integration is to find area......

Introduction to Integration

Integration is a way of adding slices to find the whole.

Integration can be used to find areas, volumes, central points and many useful things. But it is easiest to start with finding the area under the curve of a function like this:

What is the area under y = f(x) ? 

Slices

We could calculate the function at a few points and add up slices of width Δx like this (but the answer won't be very accurate):
We can make Δx a lot smaller and  add up many small slices(answer is getting better):
And as the slices approach zero in width, the answer approaches the true answer. We now write  dx to mean the Δx slices are approaching zero in width.