Struggling to understand the fundamental theorem of calculus conceptually

[Kyle.B]

I'm a first-year engineering student struggling with the conceptual leap in my calculus course, specifically with understanding the fundamental theorem of calculus and how differentiation and integration are inverse processes beyond just the mechanical steps of solving problems. I can follow the procedures for derivatives and integrals, but when it comes to applying them to real-world problems like calculating work or rates of change in my physics class, I feel lost because I don't have a solid intuitive grasp of what the operations actually mean. For students who successfully bridged this gap, what resources or methods helped you develop a deeper conceptual understanding of calculus? Did you find certain visualizations, practical applications, or a different textbook more helpful than just drilling through problem sets, and how much time did you dedicate to mastering the theory versus the computational techniques?