Learning from demonstration (LfD), which provides a natural way to transfer skills to robots, has been extensively researched for decades, and an army of methods and applications have been developed and investigated for learning an individual or low-level task. Nevertheless, learning long time sequential tasks is still very difficult as it involves task segmentation and sub-task clustering under an extremely large demonstration variance. Besides, the representation problem should be considered when doing segmentation. This paper presents a new unified framework to solve the problems of segmentation, clustering, and representation in a sequential task. The segmentation algorithm segments unstructured demonstrations into movement primitives (MPs). Then, the MPs are automatically clustered and labeled so that they can be reused in other tasks. Finally, the representation model is leveraged to encode and generalize the learned MPs in new contexts. To achieve the first goal, a change-point detection algorithm based on Bayesian inference is leveraged. It can segment unstructured demonstrations online with minimum prior knowledge requirements. By following the Gaussian distributed assumption in the segmentation model, MPs are encoded by Gaussians or Gaussian mixture models. Thus, the clustering of MPs is formulated as a clustering over cluster (CoC) problem. The Kullback-Leibler divergence is used to measure similarities between MPs, through which the MPs with smaller distance are clustered into the same group. To replay and generalize the task in novel contexts, we use task-parameterized regression models such as the Gaussian mixture regression. We implemented our framework on a sequential open-and-place task. The experiments demonstrate that the segmentation accuracy of our framework can reach 94.3% and the recognition accuracy can reach 97.1%. Comparisons with the state-of-the-art algorithm also indicate that our framework is superior or comparable to their results.