DABs inherently lack the ability to ensure ZVS during light load operation. To achieve ZVS across the entire load range and enhance system efficiency, DABs are recommended to operate in the DC transformer (DCX) mode, which enables unity output voltage gain. Therefore, to widen the voltage gain range, this paper proposes a cascaded four-switch Buck-Boost (FSBB) integrated-DAB (FI-DAB). The integrated structure allows the sharing of a bridge arm between FSBB and DAB, reducing the number of utilized switches. To further reduce the system loss caused by the backflow power of DAB, optimized dual-phase-shift control with bidirectional inner phase shifts (ODPS-BIPS) modulation method is applied. Additionally, based on the DCX concept, to match the system output voltage, the output voltage of FSBB is regulated by adjusting its duty cycle with a PI compensator plus input voltage feedforward. A fast-dynamic response control method is simultaneously introduced to alter the phase shift of DAB, aiming to improve the system's transient response performance during load variations. Ultimately, experiments are conducted to validate the effectiveness of the proposed configuration and control method.