(a) The function e-x2 does not have an elementary antiderivative, andso numerical integration is the only way to evaluate the integral 01e-x2dx.Using N=4, calculate the values ofT and S for this integral, i.e.use the trapezoidal rule and Simpson's rule to approximate the integral.(b)In order to determine how good these approximations are, we need to findupper bounds on the derivatives off(x)=e-x2. Calculate the derivatives off and show M2=2 and M4=12.(c) Use the results of part (b)to estimate the errors in the approximations frompart (a), which thus gives a pretty good idea of the value of the integral.Finally, determine what value ofN would be needed to calculate thisintegral accurately to six decimal places using Simpson's rule.