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 \( x_0=a+h \).