Nowadays, mathematics teachers in K-12 strive to promote their students' mathematical knowledge and computational thinking (CT) skills. There is an increasing need for effective CT-embedded mathematics learning material and a better understanding of students' views toward them. In this work, we present the results of a research study, which included the design of a six-lesson learning activity aimed at fostering 16- to 17-year-old secondary students' CT skills in calculus lessons using the dynamic mathematics software "GeoGebra." Our goal was to investigate how students experienced the CT-embedded calculus lessons with "GeoGebra" and what challenges they faced during their interaction with the learning material and software. We collected and analyzed data from students' code in "GeoGebra," workbooks, semi-structured interviews, and questionnaires. Our findings suggest that most students mastered using CT concepts in calculus activities to a satisfactory degree and could reason about their computational solutions using "GeoGebra" and the generated graphs. Students' understanding of the mathematical content knowledge introduced was essential to complete the lesson series successfully and unnoticed gaps in prior knowledge emerged. Our study shows that students appreciate the CT-embedded calculus lessons and "GeoGebra's" exploratory approach to mathematics problems when provided with appropriate support. We conclude that an integrated approach to mathematics education and CT is viable and can contribute not only to fostering CT but also to increasing interest in mathematics.