In this paper, a new optimum integration approach for renewable energy sources (RESs) based on probabilistic bus voltage-feeder current uncertainty analysis (PVCUA) framework is proposed. The PVCUA framework composes of three stages. The cumulant method has been utilized in the framework to characterize RESs generation and loads uncertainties and relates their probabilistic information of in an optimal RESs-integrated distribution grid problem with decision variables (bus voltage - feeder current). For minimizing the buses voltage violations and feeders current fluctuations, the optimization problem is solved by the particle swarm optimization (PSO) algorithm to identify the optimal capacity and operational mode, and the best location and type of RESs considering technical constraints. The proposed algorithm and analysis on standard 33-bus distribution network is implemented using MATLAB. The probabilistic framework reduces the complexity and computational burden of RESs planning problem considering RESs installation and operation uncertainties, which is most important for any researcher in the field of RESs planning and making it very advantageous and practical