For autonomous vehicles, scene understanding is still one of the major challenges, which needs to be well handled to avoid jittery decisions and unsmooth trajectories. Furthermore, uncertainty in trajectory prediction of traffic participants directly affects decision results, and thus contributes to safety, comfort and efficiency. This article proposes an integrated decision-making and planning (DNP) framework considering the uncertainty in trajectory prediction based on Partially Observable Markov Decision Process (POMDP). A multivariate Gaussian distribution is utilized to model the propagation of uncertainty in trajectory prediction process. To plan smooth trajectories, a feasible region construction is proposed based on fine-grained decision results to bridge the gap between decision-making and planning. Simulation and experimental results confirm that the proposed framework leads to a safer and smoother trajectory compared to command-type decision outputs by increasing the safety distance by 1.27 m and reducing the curvature fluctuations by 2.08.