A number of studies have successfully developed speaker verification or presentation attack detection systems. However, studies integrating the two tasks remain in the preliminary stages. In this paper, we propose two approaches for building an integrated system of speaker verification and presentation attack detection: an end-to-end monolithic approach and a back-end modular approach. The first approach simultaneously trains speaker identification, presentation attack detection, and the integrated system using multi-task learning using a common feature. However, through experiments, we hypothesize that the information required for performing speaker verification and presentation attack detection might differ because speaker verification systems try to remove device-specific information from speaker embeddings, while presentation attack detection systems exploit such information. Therefore, we propose a back-end modular approach using a separate deep neural network (DNN) for speaker verification and presentation attack detection. This approach has thee input components: two speaker embeddings (for enrollment and test each) and prediction of presentation attacks. Experiments are conducted using the ASVspoof 2017-v2 dataset, which includes official trials on the integration of speaker verification and presentation attack detection. The proposed back-end approach demonstrates a relative improvement of 21.77% in terms of the equal error rate for integrated trials compared to a conventional speaker verification system.