The main objective of this paper is to obtain new conditions for the integral operator $F_{\alpha,\beta}(z)$ to be univalent in the open unit disk $\mathbb{U}$. This integral operator $F_{\alpha,\beta}(z)$ was considered in a recent work \cite{lbl 4}. A number of known or new univalence conditions are shown to follow upon specializing the parameters involved in our main results.