The area under the curve is a fundamental concept for students to build their understanding of the Definite Integral. This research reveals how students comprehend the area under the curve in given contextual problems and how the Hypothetical Learning Trajectory (HLT) can help students find the concept. This research follows the development research model of Gravemeijer and Cobb, which consists of three stages: preparing for the experiment, experimenting, and retrospective analysis. This research involved three students with varying abilities: low, medium, and high. Data were collected through the analysis of student work documents and in-depth interviews. The research findings indicate that students often struggle with determining the area under the curve. Students approach the area by using various polygons. With the guidance of their lecturers, students discovered that the area under the curve can be approached by partitioning the area into polygons. The more polygons used, the closer the approximation becomes. In other words, the HLT designed in this study facilitates students in understanding the concept of the area under the curve, formulated as [equation omitted].