<p>This paper reviews the literature on how failures of data integrity contribute to algorithmic discrimination in deployed AI systems. Data integrity encompasses how data is sampled, measured, labeled, documented, and maintained over time. We argue that this integrity is a major upstream determinant of whether AI systems produce discriminatory outcomes, and that the dominant model-centric framing of AI ethics has under-weighted these data-level mechanisms. We organize the review around three contributions. First, we propose a typology of data-integrity failures with three categories: representation and sampling failures, measurement and annotation failures, and provenance and maintenance failures. Second, we trace each failure type through the AI data lifecycle (collection, labeling, preprocessing, deployment, post-deployment) to show how upstream failures cascade into, and are sometimes amplified by, downstream choices. Third, we synthesize three families of mitigation (resampling and reweighting, synthetic data generation, and documentation and governance frameworks), evaluating their documented strengths, limitations, and evidence base. We argue throughout that the cascade from data-integrity failure to discriminatory outcome is probabilistic and context-dependent rather than deterministic, but that the cumulative weight of the evidence makes data integrity a necessary, though not sufficient, condition for ethical AI. We close by identifying five research gaps, each formulated with a suggested study direction.</p>