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 = $\displaystyle \int_{-\infty}^x f(u)du$

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

P(a < x < b) = $\displaystyle P(a \leq X \leq b) = P(a \leq X < b) = F(b) - F(a)$

I know that for Y~unif(A): $\displaystyle f(y) = \frac{1_A(y)}{|A|}$

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!