The answer is a shortcut using one of the fundamental rules of calculus: . In plain English, you can change the variable without changing the relationship between F and f.

So...

This makes the terms involving x constants within the context of the integral...

This accounts for the use of "t" but the answer is still off. I am not sure where the error lies.

P.S. Your LaTex contained no errors, but was quite unnecessarily long. Look at mine and see that it is actually quite simple, much like punching in expressions on a graphing calculator. Might save you some keystrokes and confusion later