Please refer to the following image.
Based on the formula, graphically speaking, to obtain the area of the region bounded between the two curves $y=f(x)$ and $y=g(x)$, I am supposed to subtract the area of the shaded region in graph $2$ from the area of the shaded region in graph $1$ so that I can get the area between the two curves.
I can understand why I should subtract that small portion (bounded by the graph $y=g(x), x=b$, and the $x$-axis), but I cannot understand subtracting the portion (which lies below the x-axis) bounded by $y=g(x)$ and $x=a$ and $x=c$, where c is the $x$-coordinate of the point where the graph $y=g(x)$ cuts the $x$-axis. I cannot understand why this must be subtracted because this portion was never part of the shaded region of $y=f(x)$ anyway! It seems as though I am subtracting something unnecessarily! Can somebody explain this, visually if possible?
Note: In both graphs $1$ and $2$, I have included the other graph in dotted lines.