Approximating smooth function on $[0,1]$ by Bernstein polynomial (interested in approximation rate in $L^2$ norm)

Page 206 of the book Bernstein Operators and Their Properties states for $f\in C^2[0,1]$: $$B_n(f,x)-f(x)=\frac{x(1-x)}{2n}f''(x)+o\left(\frac{1}{n}\right)$$

and cites

E.V. Voronovskaya, The asymptotic behavior of the approximation of functions by their Bernstein polynomials. Doklady SSSR 4, 79–85 (1932) (in Russian)