Determining Stability of a continuous time system using Laplace Transform
ROC is a strip of plane which does not contain any poles. The region is determined by the location of poles. 

The first signal, $x(t) = e^{-t} u(t)$ , has the Laplace transform $X(s) = \frac{1}{s+1}$ and its ROC is $ \mathcal{Re}\{s\} &gt; -1 $ , since $x(t)$ was defined to be causal.

The second signal, $y(t)$, is obtained by advancing $x(t)$  by $1$ unit in time. Hence $y(t) = x(t+1)$. By Laplace transform property it's seen that $Y(s) = \frac{e^{s}}{s+1}$ , and it has the same ROC with $X(s)$, since they are both right sided sequences. However, $y(t)$ is not causal despite being right sided, due to the advance of $1$ unit to the left.