This paper investigates flexible beamforming design in an integrated sensing and communication (ISAC) network with movable antennas (MAs). A bistatic radar system is integrated into a multi-user multiple-input-single-output (MU-MISO) system, with the base station (BS) equipped with MAs. This enables array response reconfiguration by adjusting the positions of antennas. Thus, a joint beamforming and antenna position optimization problem, namely flexible beamforming, is proposed to maximize communication rate and sensing mutual information (MI). The fractional programming (FP) method is adopted to transform the non-convex objective function, and we alternatively update the beamforming matrix and antenna positions. Karush-Kuhn-Tucker (KKT) conditions are employed to derive the close-form solution of the beamforming matrix, while we propose an efficient search-based projected gradient ascent (SPGA) method to update the antenna positions. Simulation results demonstrate that MAs significantly enhance the ISAC performance when employing our proposed algorithm, achieving a 59.8% performance gain compared to fixed uniform arrays.