Find the total area between the curve y=f(x)= x^2 + 2 x - 8 and the x-axis, for x between x=-5 and x=7. by 'total area' we mean the sum of the areas of the physical regions which lie between the curve and the x-axis for -5 \le x \le 7, regardless of whether the curve is above or below the x-axis. see the linked example.