It’s all in the name right (but also the formula haha).

Cumulative Density Function represents the probability that the random variable X takes on a value less than or equal to (little) x. Note that it is not the same as it being the probability of it taking the value x.

For getting the values of a specific interval, or a single value (depending on whether it’s continuous or discrete) you might want to look into the PDF and PMF, respectively.

I’ll say with the continuous ones it’s good at least having a high-level understanding of what the calculus is doing to have a clear picture of what the different functions aim to do. No need to do double or triple integrals by hand, but it’s at least useful to know why they’re used.