I need to solve a definite integral that's a part of a larger system I have in Mathematica, but I can't use a solver to do it (something weird is happening when I use NIntegrate[...] and Integrate[...] with this solver, so to have more control I want to write it out myself). I don't know how to do this and just need an example to go on. How would you write a code that solves $\int Sin(y)dy$ (integral is from 0 to x)? The method it uses for solving doesn't really matter, although my go-to would be the Riemann sum. I feel like this should be simple, but I can't figure out how to get started.