(a) With a programmable calculator or computer, compute the left and right Riemann sums for the function $f(x)=\sin(x^2)$ on the interval [0, 1] with $n = 100$. Give your answer correct to five decimal points.

$L_{100} =$

$R_{100} =$

(b) Using the answers to (a), in which interval does the exact value of $\int_{0}^{\,1} {\sin(x^2)}\, dx$ lie?

A. $[0.295,0.306]$
B. $[0.315,0.324]$
C. $[0.333,0.342]$
D. $[0.324,0.333]$
E. $[0.306,0.315]$