A system having impulse response $ h(t)=u(t) $ stable or not? I know that for a system to be BIBO stable its impulse response must be absolutely integrable and the impulse response $ h(t)= u(t)$ integrates to approach infinity (i guess)
I proceeded as$$ \int_{-\infty}^{\infty}|u(t)|dt $$
$$ =\int_{0}^{\infty}dt $$
$$ =t\Big|_0^{\infty} $$
$$ =\infty$$
So the system must be unstable right? I m unsure  Can anyone explain in terms of poles of the $H(s)$?
Your derivation is correct. The impulse response is not absolutely integrable, hence the system is not BIBO stable. From the corresponding transfer function $H(s)=1/s$, you can see that there is a single pole at the origin. Systems with single poles on the imaginary axis, like the integrator in your example, are also called marginally stable. These systems are not BIBO stable, transients do not decay, and certain inputs can cause unbounded outputs.