In this paper, the possibility of improving target detection performance in passive bistatic radar by exploiting a frequency agile (FA) signal is investigated, namely frequency agile signal-based passive bistatic radar (FAPBR) coherent integration. Since the carrier frequency of each pulse signal is agile, FAPBR coherent integration suffers from the problems of random range and Doppler phase fluctuations. To tackle these challenges, a novel FA signal coherent integration target detection scheme for PBR is proposed. In particular, the phase quadratic difference principle is presented for eliminating Doppler phase hopping. Then, frequency rearrangement is adopted to compensate for random range phase fluctuation while obtaining the high-range-resolution profiles (HRRPs) of the detecting target. Further, we innovatively present a sliding-range ambiguity decoupling (S-RAD) method to remove the range ambiguity effect in the case of the high pulse repetition frequency (HPRF). Compared with the existing methods, the proposed method can effectively mitigate Doppler phase hopping without requiring prior target velocity information, offering improved coherent integration performance in frequency agile signals with reduced computational complexity. Moreover, it successfully corrects the range ambiguity issue caused by HPRF. Finally, a series of simulation results are presented to demonstrate the effectiveness of the proposed algorithm.