Cumulative distribution function, integration problem Given the continuous Probability density function $f(x)=\begin{cases} 2x-4, & 2\le x\le3  \\ 0 ,& \text{else}\end{cases}$
Find the cumulative distribution function $F(x)$.
The formula is $F(x)=\int _{ -\infty  }^{ x }{ f(x) } $

My Solution 
The first case is when $2\le x\le3$  then $$\int_2^x {(2u-4)} \, du=[u^2-4u]_2^x=x^2-4x-4+8=x^2-4x+4$$

so $F(x)=x^2-4x+4 , \text{ for } 2\le x\le 3$
 
The Problem
Now I have the cases where $x<2 \text{ and } x>3$ , ($\int_{-\infty}^{x}0 \, dx$) but I am not sure how to do it. I would appreciate if someone could show me the solution of this two cases.  

when x<2, it is $\int_{-\infty}^{x}0du=0$ 
when x>3, it is obviously 1. You should research the properties of $F(x)$
