The advent of cloud computing technologies shows great promise for web engineering and facilitates the development of flexible, distributed, and scalable web applications. Data integration can notably benefit from cloud computing because integrating web data is usually an expensive task. This paper introduces CloudFuice, a data integration system that follows a mashup-like specification of advanced dataflows for data integration. CloudFuice's task-based execution approach allows for an efficient, asynchronous, and parallel execution of dataflows in the cloud and utilizes recent cloud-based web engineering instruments. We demonstrate and evaluate CloudFuice's applicability for mashup-based data integration in the cloud with the help of a first prototype implementation.