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In this paper, using a very general Cameron--Storvick theorem on the Wienerspace $C_0[0,T]$, we establish various integration by parts formulas involvinggeneralized analytic Feynman integrals, generalized analytic Fourier--Feynmantransforms, and the first variation (associated with Gaussian processes) offunctionals $F$ on $C_0[0,T]$ having the form$F(x)=f(\langle{\alpha_1,x}\rangle, \ldots, \langle{\alpha_n,x}\rangle)$ forscale almost every $x\in C_0[0,T]$, where $\langle{\alpha,x}\rangle$ denotesthe Paley--Wiener--Zygmund stochastic integral $\int_0^T \alpha(t)dx(t)$, and$\{\alpha_1,\ldots,\alpha_n\}$ is an orthogonal set of nonzero functions in$L_2[0,T]$. The Gaussian processes used in this paper are not stationary.

Parts formulas involving the Fourier-Feynman transform associated with Gaussian process on Wiener space