For a function g(t), it is given that $$\int\limits_{ - \infty }^{ + \infty } {g\left( t \right){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2}}}} $$     for any real value $$\omega .$$  If $$y\left( t \right) = \int\limits_{ - \infty }^t {g\left( \tau \right)d\tau ,} $$    then $$\int\limits_{ - \infty }^{ + \infty } {y\left( t \right)dt} $$   is . . . . . . . .

A. 0

B. $$ - j$$

C. $$ - \frac{j}{2}$$

D. $$\frac{j}{2}$$

Answer: Option B