More formal expressions for the local and global errors are for the local error $$ \begin{equation*} \int_a^bf(x)dx -\frac{b-a}{6}\left[f(a)+4f((a+b)/2)+f(b)\right]=-\frac{h^5}{90}f^{(4)}(\xi), \end{equation*} $$ and for the global error $$ \begin{equation*} \int_a^bf(x)dx -S_h(f)=-\frac{b-a}{180}h^4f^{(4)}(\xi). \end{equation*} $$ with \( \xi\in[a,b] \) and \( S_h \) the results obtained with Simpson's method.