In this paper, we use a generalized Brownian motion to define a generalized analytic Feynman integral. We then obtain some results for the generalized analytic Feynman integral of bounded cylinder functionals of the form F(x) = $hat{v}$(($g_1,x)^{sim}$,..., $(g_n,x)^{sim}$) defined on a very general function space $C_{a,b}$[0,T]. We also present a change of scale formula for function space integrals of such cylinder functionals.