With their fast development and deployment, a large number of cloud services provided by distributed cloud data centers have become the most important part of Internet services. In spite of numerous benefits, their providers face some challenging issues, e.g., dynamic resource scaling and power consumption. Workload prediction plays a crucial role in addressing them. Accuracy and fast learning are the key performances. Its consistent efforts have been made for their improvement. This paper proposes an integrated prediction method that combines the Savitzky-Golay filter and wavelet decomposition with stochastic configuration networks to predict workload at the next time slot. In this approach, a task time series is first smoothed by the SG filter, and the smoothed one is then decomposed into multiple components via wavelet decomposition. Based on them, an integrated model is, for the first time, established and can well characterize the statistical features of both trend and detailed components. Experimental results demonstrate that it achieves better prediction results and faster learning speed than some representative prediction methods.