Hi Gianluca,
Thanks a lot for the reply.
Can you explain why the last integral is still not piecewise-expanded?
f[intervals_] :=
Function[{x},
Evaluate[
Plus @@ Map[
Function[{a, b, c}, UnitStep[x - a] UnitStep[b - x] c] @@ # &,
intervals]]];
g = f[{{0, 1, 1}, {2, 3, -1}, {4, 5, -1}}];
Clear[t];
ig[t_] = PiecewiseExpand@
Integrate[g[p], {p, 0, t}, Assumptions -> Element[t, Reals]]
Clear[t];
iig[t_] =
PiecewiseExpand @
Integrate[ig[q], {q, 0, t}, Assumptions -> Element[t, Reals]]
Clear[t];
iiig[t_] =
PiecewiseExpand @
Integrate[iig[q], {q, 0, t}, Assumptions -> Element[t, Reals]]
Clear[t];
Plot[{g[t], ig[t], iig[t], iiig[t]}, {t, 0, 10}]