This position paper discusses the design of an approach to enable trusted data integration in a multi-cloud environment in the presence of heterogeneous and large data sources. This approach is based on mechanisms to compute trust in data and its providers by applying statistical and probabilistic methods on its provenance. The result is a solution expressing analytics queries as services coordination that can be enacted on multi-cloud settings. This paper describes the associated challenges and possible ways of addressing them. The approach and challenges are based on concrete requirements stemming from a medical scenario related to understanding, modelling, and predicting patients' conditions associated with sleep apnoea.