Data integration from multiple autonomous data sources has emerged as an important practical problem. The key requirement for such data integration is that owners of such data need to cooperate in a competitive landscape in most of the cases. The research challenge in developing a query processing solution is that the answers to the queries need to be provided while preserving the privacy of the data sources. In general, allowing unrestricted read access to the whole data may give rise to potential vulnerabilities as well as may have legal implications. Therefore, there is a need for privacy preserving database operations for querying data residing at different parties. In this paper, we propose a new query processing technique using third parties in a peer-to-peer system. We propose and evaluate two different protocols for various database operations. Our scheme is able to answer queries without revealing any useful information to the data sources or to the third parties. Analytical comparison of the proposed approach with other recent proposals for privacy-preserving data integration establishes the superiority of the proposed approach in terms of query response times.