Concept question on using integrals to find displacement!

1. Jan 19, 2009

1. The problem statement, all variables and given/known data

I was reading a solution to the following question:

Given v(t) = 22 + 18 t, use calculus to determine the total displacement from t initial= 1.5 s to t final = 3.1 s

2. Relevant equations

Here are the steps in the equation:
I get everything up to the last part, where we take get (3.1^2 - 1.5^2)... Why is that we don't do (3.1-1.5)^2 instead? I had always imagined the it would be $$\Delta$$t squared, so just final minus initlal, then squaring the result, and not the final time squared minus initial time squared.