One way would be to use Fubini's theorem. Start with the fact that . The justification for that is that is dominated by and therefore integrable over ; and the integral is equal to

Integrate with respect to t to see that . Now use Fubini to change the order of integration and deduce that (after replacing T by t).

Now repeat the process: integrate from t=0 to T again, use Fubini, and conclude that . Finally, integrate by parts to see that .