  Let $K=\mathbb Q(\theta)$ be an algebraic number field with $\theta$ a root
of an irreducible trinomial $f(x)=x^6+ax+b$ belonging to $\mathbb{Z}[x]$. In
this paper, for each prime number $p$ we compute the highest power of $p$
dividing the discriminant of $K$ in terms of the prime powers dividing $a,~b$
and discriminant of $f(x)$. An explicit $p$-integral basis of $K$ is also given
for each prime $p$ and a method is described to obtain an integral basis of $K$
from these $p$-integral bases which is illustrated with examples.
