If We Approximate $\int_{1}^{\infty} \frac{1}{x^{2}+1} d x$ With $\int_{1}^{b} \frac{1}{x^{2}+1} d x$

Multiple Choice

If we approximate $\int_{1}^{\infty} \frac{1}{x^{2}+1} d x$ with $\int_{1}^{b} \frac{1}{x^{2}+1} d x$ what value of b could we use to estimate the value of $\int_{1}^{\infty} \frac{1}{x^{2}+1} d x$ with an error of less than 0.01? Of the following, select the smallest value of b that will work.

A) 50
B) 125
C) 250
D) 500