Find the Laplace transformation of the piecewise function.

f(t) = t+1, 0≤t≤1

f(t) = t^2, t>1

Sketch the graph of f(t)

i use the g(t)[u(t-a)-u(t-b)] and i get:

(t+1)[u(t-0)-u(t-1)]+(t^2)u(t-1)

and that gives:

(t+1)-(t+1)u(t-1)+(t^2)u(t-1)

and then i can take the Laplace

L[t]+L[1]+L[(t+1)u(t-1)]+L[(t^2)u(t-1)]

after much calculation i got answer which was wrong

I'm pretty sure i messed up trying to take the laplace of "L[(t+1)u(t-1)]+L[(t^2)u(t-1)]"

Any help?