I'm having trouble understanding the reasoning behind the $u(t)$ in some solutions, maybe I missed some fundamentals from my professor's lectures. The context is 'causal LTI systems' with impulse response $h(t)$ from $H(s)$.
For a simple example,
$$H(s) = \frac{1}{1+s^2}$$
With inverse Laplace, I expect the solution to be:
$$h(t) = \sin(t)$$
However, my professor shows in his examples that: $$h(t) = \sin(t)\ u(t)$$
I understand that the $u(t)$ can also be 1 in the t-domain, but why does it seem to not apply to all solutions using Laplace transforms then? Is it because of a causal LTI system?