This paper addresses the nature of data and knowledge, the relation between them, the variety of views as a characteristic of Big Data regarding that data may come from many different sources/views from different viewpoints, and the associated essential issues of data provenance, knowledge provenance, scientific computing integrity, and trust in the data science process. Towards the direction of data-intensive science and engineering, it is of paramount importance to ensure Scientific Computing Integrity (SCI). A failure of SCI may be caused by malicious attacks, natural environmental changes, faults of scientists, operations mistakes, faults of supporting systems, faults of processes, and errors in the data or theories on which a research relies. The complexity of scientific workflows and large provenance graphs as well as various causes for SCI failures make ensuring SCI extremely difficult. Provenance and trust play critical role in evaluating SCI. This paper reports our progress in building a model for provenance-based trust reasoning about SCI.