Functions

Let $f:[0,1] \rightarrow[0,1]$ 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?