Let \({\mathcal A}\) be the class of functions \(f\), which are holomorphic in the unit disc \(U= \{z:|z|< 1\}\), of the form \(f(z)= z+ a_2z^2+\cdots+ a_n z^n+\cdots\), \(z\in U\), and denote \({\mathcal B}(\alpha)= \{f\in{\mathcal A}: \text{Re\,}f'(z)> \alpha\}\) the class of functions of bounded turning, \(0\leq \alpha< 1\). For the Libera integral operator \(F\) given by \[ F(z)= (2/z) \int^z_0 f(t)\,dt= z+ {2\over 3} a_2 z^2+\cdots+ 2/(k+ 1) a_kz^k+\cdots \] denote the partial sums by \[ F_n(z)= z+{2\over 3} a_2z^2+\cdots+ 2/(n+ 1)\, a_n z^n. \] In this note the authors prove that for \(t\in{\mathcal B}(\alpha)\), \({1\over 4}\leq\alpha< 1\), \(F_n(z)\in{\mathcal B}(\alpha)\). For related results published in the same period see also [S. S. Miller and P. T. Mocanu, J. Math. Anal. Appl. 276, No. 1, 90–97 (2002; Zbl 1012.30012)].