In this paper we present IBIS (Internet-Based Information System), a system for the semantic integration of heterogeneous data sources, which adopts innovative and state-of-the-art solutions to deal with all aspects of a complex data-integration environment, including query answering under integrity constraints and limitations on source access. IBIS is based on the global-as-view approach, using a relational mediated schema to query the data at the sources. Sources are wrapped so as to provide a relational view on them. A key issue is that the system allows the specification of integrity constraints (modeling constraints in the domain of interest) in the global schema. Since sources are autonomous, the extracted data in general do not satisfy the constraints. IBIS adapts and integrates the data extracted from the sources making use of the constraints in the global schema, so as to answer queries at best with the information available. IBIS deals with limitations in accessing data sources, and exploits techniques developed for querying sources with access limitations in order to retrieve the maximum set of answers. In particular, it may use integrity constraints available on the sources to improve the efficiency of the extraction process.