Web has brought forth opportunities to connect information sources across all types of boundaries. The information sources include databases, XML documents, and other unstructured sources. Data integration is to combine data residing at different sources and providing the user with a unified view of these data. Currently users are expecting more efficient services from such data integration systems. Indeed, querying multiple data sources scattered on the web encounters many barriers for achieving efficiency due to the heterogeneity and autonomy of the information sources. This paper describes a query optimizer, which uses constraints to semantically optimize the queries. The optimizer first translates constraints from data sources into constraints expressed at the global level, e.g., in the common schema, and stores them in the constraint repository, again, at the global level. Then the optimizer can use semantic query optimization technologies including detection of empty results, join elimination, and predicate elimination to generate a more efficient but semantically equivalent query for the user. The optmizer is published as a web service and can be invoked by many data integration systems. We carry out experiments using our semantic query optimizer and first results show that performance can be greatly improved.