ABSTRACT
This chapter discusses the main ideas of integral calculus and the fundamental theorem of calculus. The interpretation of a definite integral is an important skill, and students should be familiar with area, volume, and motion applications, as well as with the use of the definite integral as an accumulation function. The vast majority of calculus courses use the limit definition instead of the infinitesimals one. One pro for the limit definition of integral is that limits are important in higher level mathematics classes, so students might as well start getting ready for that in calculus. Researchers have found a variety of abilities and understandings students need in order to meaningfully interpret and model with integrals. Interpreting and modelling with integrals requires reasoning using quantities, not just using bare numbers and meaningless globs of symbols. The fundamental theorem of calculus (FTC) is the most important and profound idea in calculus.
