Doing integral calculus is not easy for most students, and the way it is commonly taught in schools has attracted considerable criticism. In this paper we argue that stock-flow models have the potential to improve this state of affairs. We summarize and interpret previous research and the results of some of our own studies to explore how an intuitive understanding of (and teaching) integral calculus might be possible, based on such stock-flow models: They might be used for doing "visual integration" without calculations. Unfortunately, stock-flow tasks themselves seem to be quite difficult to solve for many people, and most attempts to make them more intuitive and easily solvable have not met with much success. There might, however, be some potential in using animated representations. In any case, a good starting point for students to eventually be able to perform visual integration in an intuitive way and to arrive at a deeper understanding of integral calculus seems to be to present flows as a succession of changes in stocks.
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