Why the integral is zero
If you are talking about telecommunications, I assume we are talking about high frequencies.
If that is the case: 


\$\frac{1}{T} = f\$
\$\omega \gg \frac{1}{T}\$


\$−\cos(\omega T)+1\$ ranges from \$0\$ to \$+2\$, if you divide this by a big number you get approximately zero. 
To give you an idea: for a frequency around \$1\;\text{kHz}\$ (which is considered "ultra low"), the result will be AT MAXIMUM \$0.002\$.