I know that a similar question exists at here but I need further explanation so with your excuse, I am asking:
Let $F(x)$ be antiderivative of $f(x)$. Now $F(c_1) - F(c_2)$ means "The area under $f(x)$ between $c_1$ and $c_2$". Since that's the case, I thought that: "Well, if that's the case, then $F(c_1)$ may be corresponding to "the area under $f(x)$ from minus infinity to $c_1$". Because when I consider it this way, $F(c_1) - F(c_2)$ becomes equal to: "The area under $f(x)$ between $c_1$ and $c_2$". But apparently this is not true. Because when I take a function like, say $y = 5$, then its antiderivative is $5x + C$ and this function at a given point has a finite value (if $C$ is constant), unlike the "area under the function" interpretation, which is infinite (area from minus infinity to a given point). So my question is: Do "value of an antiderivative at a given point" have a casual meaning like "value of an integral" has?
P.S: I would really appreciate if you could suggest me good further readings on this.