It looks like the 8.04 result is only correct with conditions. It is a basic change of variable example. The Presentations Application's Student's Integral routines with a little help from Mathematica Integrate allow us to evaluate the integral. The integrate routine is an unevaluated Integrate that allows us to manipulate the integral. It displays as a regular integral but I'll just show the InputForm here. ChangeIntegralVariable does a substitution. We then use Integrate but with the assumptions that thr f at the endpoints are greater than zero. Mathematica does evaluate that.
The routines in the Student's Integral sub-package are: integrate, BasicIntegralTable (basic table used by students), DisplayIntegralTable, BreakoutIntegral, OperateIntegrand, ChangeIntegralVariable, IntegrateByParts, TrigonometricSubsitute, LimitsBracket, EvaluateLimitsBracket, UseIntegralTable, UseIntegrate, UseNIntegrate.
The use of integrate and UseIntegrate[assumptions] is a good method for displaying an unevaluated integral in a notebook and then evaluating it with assumptions.