  We consider additive functionals as a time and space-dependent function of a
diffusion corresponding to nonhomogeneous uniformly elliptic divergence form
operator. We show that if the function belongs to natural domain of strong
solutions of PDEs then there is a version of this function such that additive
functional is a continuous Dirichlet process for almost every starting points
of diffusion and we describe the martingale and the zero-quadratic variation
parts of its decomposition. We show also that under slightly stronger condition
on the function this property holds for every starting point. Finally, we prove
an extension of the It\^o formula.
