In order to calculate the pension you can use this expression:
$\text{amount}(1+\dfrac{\text{rate}}{100})^y$ where $y$ is years.
Set $x=1+\dfrac{\text{rate}}{100}$ you count the amount of money saved over the years as follows: $$\text{amount}\times(x^{y}+x^{y-1}+...+x^0)$$
How can the last expression be rewritten as an integral?
I think that can be written only in the form of a sum: amount* summation from 0 to y of x^n Integral would be possible only when there were very small values added each step.