For a function g(t), it is given that ^{$\int\limits_{-\infty}^{+ \infty}$}g(t) e^-jwt dt = we^-2w2 for any real value w. if y(t) = ^{$\int\limits_{-\infty}^{t}$}g(T), then ^{$\int\limits_{-\infty}^{+\infty}$}y(t) dt is

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