The authors have sharpened some estimates due to M. M. Derriennic [J. Approximation Theory 31, 325-343 (1981; Zbl 0475.41025)] on integral modification of Bernstein polynomials defined as \[ M_ n(f;x)=(\eta +1)\sum^{n}_{\nu =0}p_{\eta \nu}(x)\int^{1}_{0}p_{n\nu}(t)f(t)dt,\quad f\in L^ 1[0,1], \] where \(p_{n\nu}(x)=\left( \begin{matrix} \eta \\ \nu \end{matrix} \right)x^{\nu}(1-x)^{\eta -\nu},\) \(\nu =0,1,2,...,n\). The main results of the paper are Voronowskaja type asymptotic formula for the linear combinations \(M_ n(f;k;x)\) of the operators \(M_ n(f;x)\) and an estimate of error in the approximation of f by \(M_ n(f;k;x)\) in terms of the modulus of continuity of \(f^{(p)}\), \(1\leq p\leq 2k+2\).