Studies by Gohr et al. at Crypto 2019 and subsequent related work have demonstrated that neural networks can offer new insights into cryptanalysis. Building on this insight, we leverage neural networks to learn features closely associated with integral properties and use neural network-derived distinguishers as a benchmark for the automatic search. This approach not only confirms the value of deep learning in feature discovery but also shows that neural-guided insights can improve the performance of classical cryptanalytic methods. Neural networks motivate the development of a more effective framework for identifying integral distinguishers. Comparative results show that existing automated methods, limited by search efficiency and the large search space, often fail to locate optimal distinguishers. In contrast, neural networks can directly identify high-quality integral distinguishers and reveal associated non-random structural features that are typically missed by traditional approaches. Based on these neural-network results, we refine the meet-in-the-middle search framework, thereby improving the trade-off between accuracy and computational cost. Notably, under the assumption of full-state key XOR with independent round keys, the refined framework achieves the known theoretical upper bound for key-independent integral distinguishers on non-standard SKINNY. Integral distinguishers identified by neural networks, whose underlying non-random features are successfully interpreted through Boolean function analysis, are translated into classical forms, enhancing integral key-recovery attacks. In particular, we propose a 16-round key-recovery attack on SKINNY-n-n based on a general integral key-recovery approach, improving the best-known result by two rounds under the single-tweakey setting. Furthermore, we present the first key-recovery attacks on 18-round SKINNY-n-2n and 20-round SKINNY-n-3n using integral distinguishers in the single-tweak setting.