When finding the indefinite integral, Laurie forgot to put back the original variable. She should have written
When we use the FTC with the correct antiderivative, -ln|4 – x|, we get
The moral of Laurie's story is to keep the two steps separate when evaluating a definite integral using Way 1. First, evaluate the indefinite integral. Remember to put the original variable back in. Then, after you're all done with the indefinite integral, use the FTC. Keep your calculations for the two steps separate so you don't get mixed up!