Finding system stability
A system is stable if $ \int_{-\infty}^{\infty}  |h(t) |dt &lt; \infty$

In your case $ \int_{-\infty}^{\infty}  |h(t) |dt = \int_{-\infty}^{\infty}  |e^t \sin(-3t)u(-t)| \ dt$

Since $\sin(-3t) = -\sin(3t)$,

$ = \int_{-\infty}^{\infty} | e^t \sin(3t) u(-t)| \ dt$

$ = \int_{-\infty}^{0}  e^t |\sin(3t)| \ dt$ , $u(-t) = 1$ if $ -\infty &lt; t &lt; 0$ else $0$

$ &lt; \int_{-\infty}^{0}  e^t \ dt &lt; \infty$

So the system is stable.