Consider the polynomial $f(x) = 1 + 2x + 3x^2 + 4x^3$. Let $s$ be the sum of all distinct real roots of $f(x)$ and let $t = |s|$.

Question: The area bounded by the curve $y = f(x)$ and the lines $x = 0$, $y = 0$ and $x = t$, lies in the interval