Evaluating the integral: $\lim_{R \to \infty} \int_0^R \frac{dx}{x^2+x+2}$ Please help me in this integral:

$$\lim_{R \to \infty} \int_0^R \frac{dx}{x^2+x+2}$$
  I've tried as usually, but it seems tricky. Do You have an idea?

Thanks in advance!

$$\dfrac1{x^2+x+2} = \dfrac1{\left(x+\dfrac12 \right)^2 + \left(\dfrac{\sqrt{7}}2 \right)^2}$$
Recall that
$$\int_a^b \dfrac{dx}{(x+c)^2 + d^2} = \dfrac1d \left.\left(\arctan\left(\dfrac{x+c}d\right)\right)\right \vert_{a}^b$$
I trust you can finish it from here. You will also need to use the fact that
$$\lim_{y \to \infty} \arctan(y) = \dfrac{\pi}2$$
