Example 4. Calculate the definite integral $\int_{0}^{1} \frac{d x}{1+x^{2}}$.
Solution. We are dealing with a tabular antiderivative.

$$
\int_{0}^{1} \frac{d x}{1+x^{2}}=\left.\operatorname{arctg} x\right|_{0} ^{1}=\operatorname{arctg} 1-\operatorname{arctg} 0=\frac{\pi}{4}-0=\frac{\pi}{4}
$$

Answer. $\frac{\pi}{4}$.