How can be
$$\frac{1}{0.5}\int_0^1 t\sin{(2\pi t)}\ dt = \frac{-1}{\pi}$$
and inside this interval sin signal is defined, i.e. both its $+ive$ part and $-ive$ part of the wave is present.
Shouldn't be the above mentioned expression be $0$ because integration of sinusoid over complete interval is $= 0$.
Regards