Evidence integration is a normative algorithm for choosing between alternatives with noisy evidence, which has been successful in accounting for vast amounts of behavioural and neural data. However, this mechanism has been challenged by non-integration heuristics, and tracking decision boundaries has proven elusive. Here we first show that the decision boundaries can be extracted using a model-free behavioural method termed decision classification boundary, which optimizes choice classification based on the accumulated evidence. Using this method, we provide direct support for evidence integration over non-integration heuristics, show that the decision boundaries collapse across time and identify an integration bias whereby incoming evidence is modulated based on its consistency with preceding information. This consistency bias, which is a form of pre-decision confirmation bias, was supported in four cross-domain experiments, showing that choice accuracy and decision confidence are modulated by stimulus consistency. Strikingly, despite its seeming sub-optimality, the consistency bias fosters performance by enhancing robustness to integration noise.