The proliferation of heterogeneous data sources in many application contexts brings an urgent need for expressive and efficient data integration mechanisms. There are strong advantages to using RDF graphs as the integration format: being schemaless, they allow for flexible integration of data from heterogeneous sources; RDF graphs can be interpreted with the help of an on-tology, describing application semantics; last but not least, RDF enables joint querying of the data and the ontology. To address this need, we formalize RDF Integration Systems (RIS), Ontology Based-Data Access mediators, that go beyond the state of the art in the ability to expose, integrate and flexibly query data from heterogeneous sources through GLAV (global-local-as-view) mappings. We devise several query answering strategies, based on an innovative integration of LAV view-based rewriting and a form of mapping saturation. Our experiments show that one of these strategies brings strong performance advantages, resulting from a balanced use of mapping saturation and query reformulation.