f(t) = t
2
[u(t − 1) − u(t − 2)] − 5[u(t − 2) − u(t − 3)] + (sin t)u(t − 3)
Note that this can be further simplified as:
f(t) = t
2u(t − 1) − (5 + t
2
)u(t − 2) + (sin t + 5)u(t − 3)
We would express f(t) as
f(t) = f1(t)[u(t − t0) − u(t − t1)] + f2(t)[u(t − t1) − u(t − t2)] + +fn−1(t)[u(t − tn−2) − u(t − tn−1)] + fn(t)u(t − tn−1)
I hope this helps.
