Integral quadratic form on cubic polynomials without constant term

Let $V=\{ax^3+bx^2+cx\mid a,b,c\in\mathbb R\}$. For $f\in V$, define

$$Q(f)=\int_{-1}^{1}(f'(t))^2\,dt,$$

where $f'$ denotes the derivative of $f$. Which of the following statements is FALSE?