Plot[{3/4 (theta(x) - theta(x-1/2)) + 3/2 (theta(x-1/2) - theta(x-1)), Integrate[4/3 (theta(x) - theta(x-1/2)) + 2/3 (theta(x-1/2) - theta(x-1)), x]}, {x, 0, 1}]