g[t_] := (E^(-Abs[t]));
Plot[g[t], {t, -3*Pi, 3*Pi}]

(∫_(-∞)^∞) g[
              t]^2 \[DifferentialD]t

F[
        w_] := (∫_(-∞)^∞) g[
            t]*(E^((-I*w*
                  t))) \[DifferentialD]t

(1/(2*Pi))*(∫_(-∞)^∞) Abs[F[w]]^2 \[DifferentialD]w