Calculus often presents challenges to engineering students due to its abstract nature and lack of perceived real-world relevance. This study explores how integrating sustainability themes into a first-year calculus course can increase student engagement and foster authentic learning experiences. Within the context of an engineering program focused on circularity and global responsibility, sustainability topics were embedded into lectures, assignments, and preparatory tasks. The redesign was structured using the ADDIE instructional design model and anchored to the Sustainable Development Goals framework. Central to this process was a cocreation approach, actively involving students and faculty throughout the project. Through iterative feedback cycles, including surveys (N=40) and pre- and postcourse focus groups, we assessed the impact on student learning and engagement. Results indicate that students perceived the sustainability integration as meaningful and relevant, particularly in helping them recognize the applicability of calculus to societal challenges. While many students did not report an increased understanding of mathematical concepts, they valued the broadened perspective on how calculus can contribute to solving sustainability issues. This practice paper provides a replicable blueprint for integrating sustainability into core STEM curricula through cocreation and structured instructional design, offering insights for educators aiming to connect foundational mathematics to real-world applications.