  This manuscript investigates the classical problem of determining conditions
on the parameters $\alpha,\beta \in \mathbb{C}$ for which the integral
transform
  $$C_{\alpha\beta}[\varphi](z):=\int_{0}^{z} \bigg(\frac{\varphi(\zeta)}{\zeta
(1-\zeta)^{\beta}}\bigg)^\alpha\,d\zeta
  $$ is also univalent in the unit disk, where $\varphi$ is a normalized
univalent function. Additionally, whenever $\varphi$ belongs to some subclasses
of the class of univalent functions, the univalence features of the harmonic
mappings corresponding to $C_{\alpha\beta}[\varphi]$ and its rotations are
derived. As applications to our primary findings, a few non-trivial univalent
harmonic mappings are also provided. The primary tools employed in this
manuscript are Becker's univalence criteria and the shear construction
developed by Clunie and Sheil-Small.
