Let \( f : [0,1] \to [0,1] \) be the function defined by \( f(x) = \frac{x^3}{3} - x^2 + \frac{5}{9}x + \frac{17}{36} \). Consider the square region \( S = [0,1] \times [0,1] \). Let \( G = \{(x,y) \in S : y > f(x)\} \) be called the green region and \( R = \{(x,y) \in S : y < f(x)\} \) be called the red region. Let \( L_h = \{(x,h) \in S : x \in [0,1]\} \) be the horizontal line drawn at a height \( h \in [0,1] \). Then which of the following statements is(are) true?
