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*f*is say positive in [a,b) and negative from (b,c] where f(x) is continuous on [a,c]. Letting the area of [a,b) = A1 and (b,c] = A2 then the net area is

A1 - A2.

Question: This does not make sense to me... how can area be negative? For instance what if

*f*< 0 in its entire domain [a,b] then its entire area is negative?