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Data integration systems provide access to a set of heterogeneous, autonomous data sources through a so-called global schema. There are basically two approaches for designing a data integration system. In the global-centric approach, one defines the elements of the global schema as views over the sources, whereas in the local-centric approach, one characterizes the sources as views over the global schema. It is well known that processing queries in the latter approach is similar to query answering with incomplete information, and, therefore, is a complex task. On the other hand, it is a common opinion that query processing is much easier in the former approach. In this paper we show the surprising result that, when the global schema is expressed in the relational model with integrity constraints, even of simple types, the problem of incomplete information implicitly arises, making query processing difficult in the global-centric approach as well. We then focus on global schemas with key and foreign key constraints, which represents a situation which is very common in practice, and we illustrate techniques for effectively answering queries posed to the data integration system in this case.