Which functions of time correspond to the following Laplace transforms? What values will the time functions approach as time tends to infinity?

$$F(s)=\frac{1}{{s}^{2}-1}$$

I assumed it was a standard Laplace transformed and wrote $\mathrm{sinh}(t)$, which is unbounded when $\underset{t\to \mathrm{\infty}}{lim}\mathrm{sinh}(t)=\mathrm{\infty}$

But the expected answer is $f(t)=-0.5{e}^{-t}+0.5{e}^{t}$, why is that?

$$F(s)=\frac{1}{{s}^{2}-1}$$

I assumed it was a standard Laplace transformed and wrote $\mathrm{sinh}(t)$, which is unbounded when $\underset{t\to \mathrm{\infty}}{lim}\mathrm{sinh}(t)=\mathrm{\infty}$

But the expected answer is $f(t)=-0.5{e}^{-t}+0.5{e}^{t}$, why is that?