I'm having trouble understanding the circled part of this picture below. I see that they set $F(x) = 0$ to solve for $C$, but why were they able to plug in $1$ as opposed to any other number? it seems like a $2$ or $3$ would lead to a different value of $C$.
Also why is $F(x) = 1$ when $x \ge 4$? Is this because of some property of antiderivatives I'm forgetting?
I tried looking through my notes and finding similar examples online, but either all problems are different or they don't really explain why these two steps are taken or why they are allowed to happen.