Indefinite Integration: Explaining the Point Behind It

[Bashyboy]

Presently, I am reading about computing definite integrals; and in one of the examples the authors provides, there is a statement made: "Recall that the point behind indefinite integration...is to determine what function we differentiated to get the integrand."

I was wondering if someone could perhaps explain this to me?

 

[grzz]

... "Recall that the point behind indefinite integration...is to determine what function we differentiated to get the integrand."

I was wondering if someone could perhaps explain this to me?

Here is an example:

∫xdx = \frac{x^{2}}{2} + constant
The reason for this is because \frac{d(\frac{x^{2}}{2} + constant)}{dx} = 2x/2 + 0 = x.

i.e. in an indefinite integration (like the above) we try to find the function, that when differentiated, will give what we are going to integrate.