Let P (x) be a real polynomial of degree 3 which vanishes at x=-3. Let P (x) have local minima at x=1, local maxima at x=-1 and ∫_-1^1 P (x) d x=18,…

Let $\displaystyle \mathrm{P}(x)$ be a real polynomial of degree $\displaystyle 3$ which vanishes at $\displaystyle x=-3$. Let $\displaystyle \mathrm{P}(x)$ have local minima at $\displaystyle x=1$, local maxima at $\displaystyle x=-1$ and $\displaystyle \int_{-1}^1 \mathrm{P}(x) \mathrm{d} x=18$, then the sum of all the coefficients of the polynomial $\displaystyle \mathrm{P}(x)$ is equal to \_\_\_\_.