Students’ reasoning about how quantities vary in tandem plays an important role  in the students’ success in learning calculus in Indonesia. This study reports the investigation of how students’ reason during their studies concerning two covarying quantities in integral problem. High performing 2nd term calculus students were chosen to solve problems that involved interpreting and representing how quantities change in tandem. Interviews were conducted to reveal the students’ reasoning while solving covariational problems. This investigation points out that students were able to construct the relation of dependent variable that changes in tandem with the independent variable. However, students appeared to have difficulty in forming images of continuously changing rates and could not accurately apply the  concept of integrals. These findings suggest that learning in calculus should place increased emphasis on coordinating images of two quantities changing in tandem about instantaneous rate of change and to promote conceptual knowledge in integral technique.