We first need to determine the intersection points of the given curves. To do so, let us equate them:

The points satisfying the last equation are -2, 0, 2. Since there is an extra condition of x≥0, the points
of intersection are 0 and 2. Also, in the interval 0≤x≤2, we have 

and therefore the required area A is evaluated as

Therefore the correct answer is the C option.