$F\left(s\right)=L\left[1\right]\left(s\right)={\int}_{0}^{\infty}{e}^{-st}dt=\frac{{e}^{-st}}{s}{|}_{0}^{\infty}=\frac{-1}{s}({e}^{-\infty}-{e}^{0})=\frac{1}{s}$

$F\left(s\right)=L\left[1\right]\left(s\right)={\int}_{0}^{\infty}{e}^{-st}dt=\frac{{e}^{-st}}{s}{|}_{0}^{\infty}=\frac{-1}{s}({e}^{-\infty}-{e}^{0})=\frac{1}{s}$