In this paper, we introduce a new concept of a generalized analytic Feynman integral combining the bounded linear operators on abstract Wiener space. We then obtain some Feynman integration formulas involving the generalized first variation. These formulas are more generalized forms rather than the formulas studied in previous papers. Finally, we establish a generalized Cameron-Storvick theorem, and give some examples to illustrate the usefulness of our results and formulas.