A) Evaluate the following integrals using both Trapezoidal rule and Simpson rule and calculate the error bounds with equal interval size is (12 + a).

b) Find the value of integrals using both Trapezoidal rule and Simpson rule for the following integrals with the maximum error bound is 0.00000001. (Hint: first find the equal interval size using the given error bound value.)
I *** sin(ax?) dx
II. 42 atsinadx

c) The error function is given by erf(x) = le-dt. Note that it is difficult to get an exact value for erf(x) since we don't know an anti derivative for e-". Given that, erf(0.25) = 0.27633, erf(0.5) = 0.52050 erf(1) = 0.84270, Calculate the p2(x), correct to 5 decimal places that approximates erf(x). Use it to approximate erf (0.75). Using the error formula for Lagrange Interpolation, give bounds on your estimation of erf (0.75). [Hint: The following fact from Calculus is useful: If f(x) = g(x) dx then f'(x) = g(x)] Please solve it step by step and explain specific steps. I want to understand how to solve. (Clear steps and little explanation is required, not just the answer)Take a=2 and b=3.