Maybe that’s not universal, but the way the notation was taught to me in school (Germany) was that the finite sum Σf(x)Δx is simply written as ∫f(x)dx in the li

Maybe that’s not universal, but the way the notation was taught to me in school (Germany) was that the finite sum Σf(x)Δx is simply written as ∫f(x)dx in the limit. So dx is really just an infinitesimal Δx, and ∫ is the summation symbol, only written with a large Latin (as opposed to the usual Greek) “S”. That’s useful to know because several integration tricks become easy if you keep that relationship in mind. If you can transform a sum, you can transform the corresponding integral. (With the usual caveats around degenerate cases.) Similarly, for differentiation, the limit of Δy/Δx is written as dy/dx. Again, knowing this enables you to derive otherwise complicated looking transformations.