In this paper, we first establish an Ito formula for a finite quadratic variation process X expanding f(t,X-t), when f is of class C-2 in space and is absolutely continuous in time. Second, via a Fukushima-Dirichlet decomposition we obtain an explicit chain rule for f(t,X-t), when X is a continuous semimartingale and f is a "quasi-strong solution" (in the sense of approximation of classical solutions) of a parabolic PDE. Those results are applied in a companion paper to establish a verification theorem in stochastic differential games.