> Lets say you need to find the probability of something happening 10% of the time to 40% of the time, you need to perform definite integration of the curve ( lets say normal curve ) from 0.1 to 0.4 on the x axis multiplied by the normal curve function.

No one does this in the real world. Not even professional statisticians who know calculus. In the old days they used table lookups. Today they use software.

You need to understand the concept of areas under curves. Calculus is just a means to compute the area.