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 $\xi \in [a,b]$.