mark
The midpoint rule for numerical integration states
\int_a^b f(x)\,dx \approx \sum_{i=1}^n f\left(\frac{x_{i-1}+x_i}{2}\right)\Delta x,
where x_i=a+i\Delta x and \Delta x = (b-a)/n.
Use a first order Taylor series approximation to f to derive an upper bound for the error in this approximation.