$$y(s)=1/s-1/{s}^{2}+\mathrm{exp}(-s)\cdot (1/{s}^{2})$$

I'm struggling with

$$\mathrm{exp}(-s)\cdot (1/{s}^{2})$$

formulas:

$$f(t-1)u(t-1)\to \mathrm{exp}(-s)F(s)$$

But

$$f(t)=t\cdot u(t)$$

is this true: inverse Laplace transform of

$$\mathrm{exp}(-s)F(s)=(t-1)u(t-1)u(t-1)$$

I'm struggling with

$$\mathrm{exp}(-s)\cdot (1/{s}^{2})$$

formulas:

$$f(t-1)u(t-1)\to \mathrm{exp}(-s)F(s)$$

But

$$f(t)=t\cdot u(t)$$

is this true: inverse Laplace transform of

$$\mathrm{exp}(-s)F(s)=(t-1)u(t-1)u(t-1)$$