This means that the global error goes like \( \approx O(h^2) \). The trapezoidal reads then $$ \begin{equation} I=\int_a^bf(x) dx=h\left(f(a)/2 + f(a+h) +f(a+2h)+ \dots +f(b-h)+ f_{b}/2\right), \tag{4} \end{equation} $$ with a global error which goes like \( O(h^2) \).

Hereafter we use the shorthand notations \( f_{-h}=f(x_0-h) \), \( f_{0}=f(x_0) \) and \( f_{h}=f(x_0+h) \).