In this article several tasks that have been designed to assess students' understanding of calculus courses on antiderivative mathematical object are presented. The tasks are designed taking into account the suggestions and recommendations of the extensive background research on teaching calculus with which it has internationally. Also, the ontosemiotic analysis of each of the proposed tasks is detailed, which gives evidence of the network of mathematical objects and processes - and their links - put into play in the activities of understanding the antiderivative. The result of this study shows that the tasks described here can be applied to college students (or calculus courses students who have studied the antiderivative), and could be adapted to address the study of the mathematical object.