Accurate polyp delineation in colonoscopy is crucial for assisting in diagnosis, guiding interventions, and treatments. However, current deep-learning approaches fall short due to integrity deficiency, which often manifests as missing lesion parts. This paper introduces the integrity concept in polyp segmentation at both macro and micro levels, aiming to alleviate integrity deficiency. Specifically, the model should distinguish entire polyps at the macro level and identify all components within polyps at the micro level. Our Integrity Capturing Polyp Segmentation (IC-PolypSeg) network utilizes lightweight backbones and 3 key components for integrity ameliorating: 1) Pixel-wise feature redistribution (PFR) module captures global spatial correlations across channels in the final semantic-rich encoder features. 2) Cross-stage pixel-wise feature redistribution (CPFR) module dynamically fuses high-level semantics and low-level spatial features to capture contextual information. 3) Coarse-to-fine calibration module combines PFR and CPFR modules to achieve precise boundary detection. Extensive experiments on 5 public datasets demonstrate that the proposed IC-PolypSeg outperforms 8 state-of-the-art methods in terms of higher precision and significantly improved computational efficiency with lower computational consumption. IC-PolypSeg-EF0 employs 300 times fewer parameters than PraNet while achieving a real-time processing speed of 235 FPS. Importantly, IC-PolypSeg reduces the false negative ratio on five datasets, meeting clinical requirements.