Schema statements in OWL are interpreted quite differently from analogous statements in relational databases. If these statements are meant to be interpreted as integrity constraints (ICs), OWL's interpretation may seem confusing and/or inappropriate. Therefore, we propose an extension of OWL with ICs that captures the intuition behind ICs in relational databases. We discuss the algorithms for checking IC satisfaction for different types of knowledge bases, and show that, if the constraints are satisfied, we can disregard them while answering a broad range of positive queries.