  For $\gamma\in\IC$ such that $|\gamma|<\pi/2$ and $0\leq\beta<1$, let
${\mathcal P}_{\gamma,\beta} $ denote the class of all analytic functions $P$
in the unit disk $\mathbb{D}$ with $P(0)=1$ and $$ {\rm Re\,} \left
(e^{i\gamma}P(z)\right)>\beta\cos\gamma \quad \mbox{ in ${\mathbb D}$}. $$ For
any fixed $z_0\in\mathbb{D}$ and $\lambda\in\overline{\mathbb{D}}$, we shall
determine the region of variability $V_{\mathcal{P}}(z_0,\lambda)$ for
$\int_0^{z_0}P(\zeta)\,d\zeta$ when $P$ ranges over the class $$
\mathcal{P}(\lambda) = \left\{ P\in{\mathcal P}_{\gamma,\beta} :\,
P'(0)=2(1-\beta)\lambda e^{-i\gamma}\cos\gamma \right\}. $$ As a consequence,
we present the region of variability for some subclasses of univalent
functions. We also graphically illustrate the region of variability for several
sets of parameters.
