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We consider additive functionals as a time and space-dependent function of adiffusion corresponding to nonhomogeneous uniformly elliptic divergence formoperator. We show that if the function belongs to natural domain of strongsolutions of PDEs then there is a version of this function such that additivefunctional is a continuous Dirichlet process for almost every starting pointsof diffusion and we describe the martingale and the zero-quadratic variationparts of its decomposition. We show also that under slightly stronger conditionon the function this property holds for every starting point. Finally, we provean extension of the It\^o formula.

On time-dependent functionals of diffusions corresponding to divergence form operators