Suppose you need to integrate some specific function f. From experimental data, you know that f''(x)=e-x2 and that\table[[x,-0.5,-0.25,0,0.25,0.5],[f(x),7.870,7.906,8.000,8.156,8.370]](a) Calculate the trapezoidal approximation T4 for the integral -0.50.5f(x)dx to 3 decimal places.(b) Find the maximum that the error might be,E(4), for the above approximation to at least 3 decimal places. The error formula for the trapezoidal approximation Tn looks like E(n)=(b-a)312n2M where M is the maximum value of |f''(x)| on the interval a,b.(c) Combining the previous two parts, determine an interval which is guaranteed to contain the true value of the integral. Provide 3 decimal places for the endpoints.