The correct mathematical expression for the local error for the rectangular rule \( R_i(h) \) for element \( i \) is $$ \begin{equation*} \int_{-h}^hf(x)dx - R_i(h)=-\frac{h^3}{24}f^{(2)}(\xi), \end{equation*} $$ and the global error reads $$ \begin{equation*} \int_a^bf(x)dx -R_h(f)=-\frac{b-a}{24}h^2f^{(2)}(\xi), \end{equation*} $$ where \( R_h \) is the result obtained with rectangular rule and \( \xi \in [a,b] \).