Graph a polynomial and find its zeroes

A polynomial is stored as a list of coefficients, from the highest power down. You will work out its values, find its whole-number zeroes, and trap the zeroes that are not whole numbers between two whole numbers.

The idea. Horner's method: start at $0$, and for each coefficient multiply by $x$ and add the coefficient. A zero lies between $k$ and $k + 1$ when $p(k)$ and $p(k + 1)$ have opposite signs.

Your tasks.

1. In value, return $p(x)$ by Horner's method.
2. Fill zeroes with the whole numbers from $-5$ to $5$ where $x^3 - x^2 - 4x + 4$ is $0$.
3. Fill between with each $k$ from $-5$ to $4$ where $x^3 - 3x + 1$ changes sign between $k$ and $k + 1$.