Random Variables and Distribution

Let X be a random variable with distribution function F that is continuous. Show that Y = F(X) is uniform.

I'm sort of confused by what this is even asking, but I tried to put together some information.

F =

I tried to look in my book for anything and also found something:

P(a < x < b) =

I know that for Y~unif(A):

I'm not sure if any of this is relevant (or perhaps even right), but I was trying to put anything together because I'm just not sure what to do. Any help would be appreciated. Thank you!