Help with Continuous Random Variables?

I'm given the following density function:

f(x) = (3/2)sqrt(x) ; 0<x<1

0 ; elsewhere

Find F(x)

I did the integration, and what I came up with was

F(x) = 0 ; x #< 0 (please note: I'm using the # to mean "or equal to")

x^(3/2) ; 0<x<1

1 ; x #>1

This is pretty close, however, the correct answer has different # placements:

F(x) = 0 ; x < 0

x^(3/2) ; 0#<x<1

1 ; x #>1

I don't understand what I'm doing wrong. If f(x) is 0 until x goes ABOVE zero, then why does F(x) say x has to be BELOW zero to create F(x)=0, and x^(3/2) starts at zero?

I hope this isn't too confusing, I wasn't entirely sure how else to word it. Any help is greatly appreciated.