If $\int \limits_0^b \large\frac{dx}{1+x^2}$$=\int \limits_b^{\infty} \large \frac{dx}{1+x^2},$ then $b=$

Question

$$(a)\;\tan ^{-1}\bigg(\frac{1}{3}\bigg)\quad (b)\;\frac{\sqrt 3}{2} \quad (c)\;\sqrt 2 \quad (d)\;1$$