How can I build intuition for definite integrals beyond area under the curve?

[Victoria_A]

I'm a first-year engineering student struggling to truly grasp the conceptual leap from basic differentiation to integration in my calculus course. I can follow the mechanical steps for power rule and u-substitution, but I'm having trouble visualizing what the definite integral actually represents beyond "area under the curve," especially when applied to real-world problems like calculating work or fluid flow. For those who moved past rote memorization, what resources or analogies helped you build a stronger intuitive understanding of integration? Did focusing on the Fundamental Theorem of Calculus as a unifying concept clarify things, or was it something else, like physical applications or graphical interpretations, that made it click?