Substitution Rule for Definite Integrals

Now we need to go back and revisit the substitution rule as it also applies to definite integrals.  At some level there actually isn't a lot to do in this section. The first step in doing a definite integral is to calculate the indefinite integral and that hasn't modified.  Still we will compute the indefinite integral first. It means that we already know how to do these. We utilize the substitution rule to determine the indefinite integral & then do the evaluation.

However there are, two ways to deal along with the evaluation step.  One way doing the evaluation is the possibly the most obvious at this point, however also has a point in the process where we can obtain in trouble if we aren't paying attention.