A function $\mathrm{f}$ is defined by $\mathrm{f}(x)=a x^3+b x^2+c x+d$. The graph of $y=\mathrm{f}(x)$ passes through the points $(1,5)$ and $(-1,-3)$. The graph has a turning point at $x=1$, and $\int_0^1 \mathrm{f}(x) \mathrm{d} x=6$.
Find the values of $a, b, c$ and $d$.