A. Estimate $\int_0^1\,1/(1+x^2)\,dx$ by subdividing the interval into 8 parts, using
(i) the left Riemann sum: $\int_0^1\,1/(1+x^2)\,dx \approx$
(ii) the right Riemann sum: $\int_0^1\,1/(1+x^2)\,dx \approx$
(iii) the trapezoid rule $\int_0^1\,1/(1+x^2)\,dx \approx$

B. Since the exact value of this integral is ${1\over 4} \pi$, you can use your result from A to estimate the value of $\pi$. Be sure you can explain why your first estimate is too large and the second too small.