Suppose we divide the interval $[1,4]$ into $100$ equally wide subintervals and calculate a Riemann sum for f$($x$)=1+$ x$^2$ by randomly selecting a point ci in each subinterval. We can be certain that the value of the Riemann sum is within what distance of the exact value of the area between the graph of f and the interval $[1,4]?($b$)$ What if we take $200$ equally long subintervals?