Do you know what a Riemann sum is ? If, so just think of a definite integral as another way of compute the Riemann sum over some interval fairly easier than just adding the term of a Riemann sum to however many sub-divisions over some interval.
Here is a link that can explain better than I can:
Pauls Online Notes : Calculus I - Definition of the Definite Integral
Also for a bit help your definite integral based on the information given
Edit: Are you writing the Riemann sum of this function? or definite integral? It seems to me, I might have misread, you are trying to write this in terms of n in the form of a definite integral, then you start to mention, the change and x and such.