function [int, err] = midpoint_demo(a, b, m)
  h = (b - a)/m;
  x = a+h/2:h:b-h/2;
  y = sin(x);
  int = h*sum(y);
  exact = -cos(b) + cos(a); % exact = int_a^b sin(x) dx
  err = abs(exact - int);
end