Question

http://prntscr.com/9of7zf

Answer 1

hint: areas above the x axis are positive and below the x axis are negative

Answer 2

if you take the absolute value however... they are always positive

Answer 3

The area between the curve and the x-axis is negative for regions A and C. Therefore, the absolute value of those areas (or, |f(x)|) is going to have the same magnitude, and will be positive.

Answer 4

What you have is something like a simple expression below.
\(\color{#000000 }{ \displaystyle (-5+6-8)+(|-5|+|6|+|-8|) }\)

Answer 5

-A+B-C+(|-A|+|B|+|-C|=-A+B-C+A+B+C=2B