If $f(t) =\int \limits _{-t}^t \large\frac{e^{-|x|}}{2}$$dx$, then $\lim \limits_{t \to \infty} f(t)$ is equal to

Question

$$\begin {array} {1 1} (a)\;1 & \quad (b)\;\frac{1}{2} \\ (c)\;0 & \quad (d)\;-1 \end {array}$$