Having performed this subdivision and polynomial approximation, one from $x_0-h$ to $x_0$ and the other from $x_0$ to $x_0+h$, $$\begin{equation*} \int_a^{a+2h}f(x)dx=\int_{x_0-h}^{x_0}f(x)dx+\int_{x_0}^{x_0+h}f(x)dx, \end{equation*}$$ we can easily calculate for example the second integral as $$\begin{equation*} \int_{x_0}^{x_0+h}f(x)dx\approx \int_{x_0}^{x_0+h}\left(\frac{x-x_0}{(x_0+h)-x_0}f(x_0+h)+\frac{x-(x_0+h)}{x_0-(x_0+h)}f(x_0)\right)dx. \end{equation*}$$