In modern information systems different information features, about the same individual, are often collected and managed by autonomous data collection services that may have different privacy policies. Answering many end-users' legitimate queries requires the integration of data from multiple such services. However, data integration is often hindered by the lack of a trusted entity, often called a mediator, with which the services can share their data and delegate the enforcement of their privacy policies. In this paper, we propose a flexible privacy-preserving data integration approach for answering data integration queries without the need for a trusted mediator. In our approach, services are allowed to enforce their privacy policies locally. The mediator is considered to be untrusted, and only has access to encrypted information to allow it to link data subjects across the different services. Services, by virtue of a new privacy requirement, dubbed k-Protection, limiting privacy leaks, cannot infer information about the data held by each other. End-users, in turn, have access to privacy-sanitized data only. We evaluated our approach using an example and a real dataset from the healthcare application domain. The results are promising from both the privacy preservation and the performance perspectives.