Struggling to set up integrals for variable-force work and centers of mass

[HannahUD]

I'm a second-year engineering student struggling with the application of integral calculus to real-world problems, specifically in calculating work done by a variable force and finding centers of mass for irregular shapes. I can follow the textbook examples, but I hit a wall when trying to set up the integrals from a word problem's description. For students or tutors who have overcome this hurdle, what strategies or resources helped you develop the intuition to translate a physical scenario into the correct integral setup, beyond just memorizing formulas?