sin x dx accurately to four decimal places. (a) Use the Maclaurin series for sin (u), substituting u=x², to write a power series for sin (x²). (b) Integrate this power series term-by-term to write a new power series for the integral sin x² dx. (c) Now evaluate the power series resulting from your integration in part (b) from x=0 to x=1, to obtain a series of constant terms. (d) Find a decimal approximation for the value of this resulting series of constant terms that is accurate to 4 decimal places. As part of your answer, you should cite a theorem justifying your claim to know that your approximation is as accurate as desired.