When using integration to find an area, exactly which "area" is found?

$I = {\int}_{a}^{b} \setminus f \left(x\right) \setminus \mathrm{dx}$
Then the Integration calculates the "net" area between the curve $y = f \left(x\right)$ from $x = a$ to $x = b$, and the $x$-axis.
By "net" area, we consider any area below the curve and above the $x$-axis to be positive , and any area above the curve and below the $x$-axis to be negative.