A coordinate-plane graph of f has these geometric regions with the x-axis from left to right: on [-4, 0], a semicircle above the x-axis with radius 2 and diameter on the x-axis; on [0, 4], a quarter circle below the x-axis with radius 4; on [4, 9], a rectangle above the x-axis with width 5 and height 2. Find ∫_{-4}⁹ f(x) dx. Give an exact answer in terms of π.