I got the following density function:
$$\begin{cases} 4e^{-4(x-1)} & \mbox{if} \; x \ge 1 \\ 0 & \mbox{if}\; x \lt 1 \end{cases} $$
Now I want to get the distribution function which I thought is
$$ \int 4e^{-4(x-1)} = -e^{-4(x-1)} $$
But I think this distribution function is wrong and I don`t know what I am missing. Thanks for any answer and comment in advance.