Crystallography is the powerhouse technique for molecular structure determination, with applications in fields ranging from energy storage to drug design. Accurate structure determination, however, relies partly on determining the precise locations and integrated intensities of Bragg peaks in the resulting data. Here, we describe a method for Bragg peak integration that is accomplished using neural networks. The network is based on a U-Net and identifies peaks in three-dimensional reciprocal space through segmentation, allowing prediction of the full 3D peak shape from noisy data that is commonly difficult to process. The procedure for generating appropriate training sets is detailed. Trained networks achieve Dice coefficients of 0.82 and mean IoUs of 0.69. Carrying out integration over entire datasets, it is demonstrated that integrating neural network-predicted peaks results in improved intensity statistics. Furthermore, using a second dataset, the possibility of transfer learning between datasets is shown. Given the ubiquity and growing complexity of crystallography, we anticipate integration by machine learning to play an increasingly important role across the physical sciences. These early results demonstrate the applicability of deep learning techniques for integrating crystallography data and suggest a possible role in the next generation of crystallography experiments.