Let $u\left ( t \right )$ denote the unit step function. The bilateral Laplace transform of the function $f\left ( t \right )=e^{t}u\left ( -t \right )$ is ________________.
- $\frac{1}{s-1}$ with real part of $s< 1$
- $\frac{1}{s-1}$ with real part of $s> 1$
- $\frac{-1}{s-1}$ with real part of $s< 1$
- $\frac{-1}{s-1}$ with real part of $s> 1$