The paper considers a measurable space of curves (sequences of states) ― equivalence classes in Skorokhod space which are invariant under change of time. We define on each class, which can be characterized by a linear ordering on a subset of the metric state space, integrals of functions with respect to additive functionals. For semi-Markov processes, we determine the Laplace transform of the probability of an interval of constancy with a given waiting time in it in terms of such integrals that depend only on the sequence of states