In the context of the joint radar and communications (JRC) framework, reconfigurable intelligent surfaces (RISs) emerged as a promising technology for their ability to shape the propagation environment by adjusting their phase-shift coefficients. However, achieving perfect synchronization and effective collaboration between access points (APs) and RISs is crucial to successful operation. This paper investigates the performance of a bistatic JRC network operating in the millimeter-wave (mmWave) frequency band, where the receiving AP is equipped with an RIS-integrated array. This system simultaneously serves multiple UEs while estimating the position of a target with limited prior knowledge of its position. To achieve this, we optimize both the power allocation of the transmitted waveform and the RIS phase-shift matrix to minimize the position error bound (PEB) of the target. At the same time, we ensure that the UEs achieve an acceptable level of spectral efficiency. The numerical results show that an RIS-integrated array, even with a small number of receiving antennas, can achieve high localization accuracy. Additionally, optimized phase-shifts significantly improve the localization accuracy in comparison to a random phase-shift configuration.