Let f : [0, 3] → R be defined by f(x) := x for 0 < x < 1, f(x) := 1 for 1 < x < 2 and f(x) := x for 2 < x < 3. Obtain formulas for F(x) := ∫x0 f and sketch the graphs of f and F. Where is F differentiable? Evaluate Fʹ(x) at all such points.