Let $T_n(h)$ be the class of analytic functions in the unit disk $E$ of the form $f(z)=a_pz^p+\sum_{n=p+1}^{\infty} a_nz^n$, $p\ge 1$, which satisfy the condition, $\dfrac{(n+1)}{(n+p)}\dfrac{D^{n+1}f(z)}{D^nf(z)}\prec h(z)$, $z\in E$, where $h$ is a convex univalent function in $E$ with $h(0)=1$. Then it is proved that $f$ is preserved under the Bernardi integral operator under certain conditions. It is also shown that if $f\in T_0(h)$, it is preserved under the Ruscheweyh integral operator under certain conditions.