One possible strategy then is to find a reliable polynomial expansion for $f(x)$ in the smaller subintervals. Consider for example evaluating $$\begin{equation*} \int_a^{a+2h}f(x)dx, \end{equation*}$$ which we rewrite as $$\begin{equation} \int_a^{a+2h}f(x)dx= \int_{x_0-h}^{x_0+h}f(x)dx. \tag{2} \end{equation}$$ We have chosen a midpoint $x_0$ and have defined $x_0=a+h$.