You are given the four points in the plane A=(−1,−8)A=(−1,−8), B=(4,5)B=(4,5), C=(8,−2)C=(8,−2), and D=(12,2)D=(12,2). The graph of the function f(x)f(x) consists of the three line segments AB, BC and CD. Find the integral ∫12−1f(x)dx by interpreting the integral in terms of sums and/or differences of areas of elementary figures.