Although current salient object detection (SOD) works have achieved significant progress, they are limited when it comes to the integrity of the predicted salient regions. We define the concept of integrity at both a micro and macro level. Specifically, at the micro level, the model should highlight all parts that belong to a certain salient object. Meanwhile, at the macro level, the model needs to discover all salient objects in a given image. To facilitate integrity learning for SOD, we design a novel Integrity Cognition Network (ICON), which explores three important components for learning strong integrity features. 1) Unlike existing models, which focus more on feature discriminability, we introduce a diverse feature aggregation (DFA) component to aggregate features with various receptive fields (i.e., kernel shape and context) and increase feature diversity. Such diversity is the foundation for mining the integral salient objects. 2) Based on the DFA features, we introduce an integrity channel enhancement (ICE) component with the goal of enhancing feature channels that highlight the integral salient objects, while suppressing the other distracting ones. 3) After extracting the enhanced features, the part-whole verification (PWV) method is employed to determine whether the part and whole object features have strong agreement. Such part-whole agreements can further improve the micro-level integrity for each salient object. To demonstrate the effectiveness of our ICON, comprehensive experiments are conducted on seven challenging benchmarks. Our ICON outperforms the baseline methods in terms of a wide range of metrics. Notably, our ICON achieves ~10% relative improvement over the previous best model in terms of average false negative ratio (FNR), on six datasets.