What area does the antiderivative represent?Consider the antiderivative of the function e − x ,,...

Explanation:
Evaluating the antiderivative at the value 0 produces −1. Now, I was taught to conceptualize an antiderivative as an area under a curve
1. An antiderivative F results from performing indefinite integration on a function f.
2. For $a<b,$, the signed area (i.e., the area residing in the positive vertical region minus the area residing in the negative vertical region) enclosed by the curve $y=f(x),$, the x-axis, and the lines $x=a$ and $x=b$ is given by the definite integral ${\int }_a^{b}f.$
3. By the Fundamental Theorem of Calculus, the above signed area ${\int }_a^{b}f$
$=F(b)-F(a).$
4. The actual area enclosed by the curve $y=f(x),$, the x-axis, and the lines $x=a$ and $x=b$ is given by ${\int }_a^b|f|,$, which does not equal $F(b)-F(a).$
5. In your Question, the value evaluation $F(0)=-1$ does not correspond to an area.