At CRYPTO 2019, A. Gohr made a breakthrough in combining classical cryptanalysis and deep learning and applied his method to round reduced SPECK successfully. However, his suggested neural-based distinguisher scheme is only limited to differential cryptanalysis. In this paper, we have the following contributions:1. We combine integral cryptanalysis and deep learning to propose our neural-based integral distinguisher scheme for the first time. To illustrate the effectiveness of our distinguisher scheme, we apply it to block ciphers of different structures, such as substitution-permutation structure ciphers (PRESENT and RECTANGLE), Feistel structure cipher (LBLOCK), and addrotate-XOR cipher (SPECK) and compare the results with the state-of-the-art classical integral distinguishing method, namely, the bit-based division property. To our great surprise, our neural network-based integral distinguisher can extend the number of distinguished rounds for all block ciphers by two additional rounds (except RECTANGLE, where it is improved by one round) under the same data complexity.2. As an additional advantage of our scheme, we demonstrate that our Neural Distinguisher (ND) is not only helpful for block cipher designers but