Determine how large the number $a$ has to be so that $$\int_{a}^{\,\infty} {\frac{1}{x^2+1}}\, dx < 0.001$$ by finding the value of $a$ such that $$\int_{a}^{\,\infty} {\frac{1}{x^2+1}}\, dx = 0.001$$

Make sure that your answer is correct to two decimal places.

$a =$