In this paper, we propose a novel integrated communication and positioning design for orthogonal frequency division multiplexing system aided by a reconfigurable intelligent surface (RIS) in indoor circumstances. The channel frequency responses on pilots (CFROPs) of places of interest are used for online mapping with the offline CFROP database. We transform the objective of minimizing the similarity of different CFROPs into creating a differentiated database by optimizing the phase coefficients of RIS. Imperfect channel state information is considered due to time-varying caused by the two-stage mapping. We formulate a universal optimization problem for maximizing either the average or the minimum virtual distance of CFROPs. The communication service requirements are converted as constraints. A moderate case is discussed to reduce computational complexity with minor accuracy loss. A special property called correlation dispersion is analyzed. It is capable of eliminating the spatial consistency that incurs inaccuracy to traditional positioning methods. The property and the moderate case complement each other well with clear and logical physical interpretation. The particular characteristic makes our design outperform others especially in high-level-noise environments. It works even better when the prior information of user's potential location is available. The validity of our design is confirmed by numerical results.