Evaluate the following integrals (1-y²) dr. (b) (1-2)- dr. (c) (2+2) - dr.

The given integral is $\int (1+r^2)^{-1} dr$, which can be rewritten as:

$$\int \frac{1}{1+r^2} dr$$

This is a standard integral form $\int \frac{1}{a^2+r^2} dr$, where $a=1$.

The integral of $\frac{1}{a^2+r^2}$ with respect to $r$ is $\frac{1}{a} \arctan\left(\frac{r}{a}\right) + C$.
Substitute $a=1$ into the formula:

$$\int \frac{1}{1^2+r^2} dr = \frac{1}{1} \arctan\left(\frac{r}{1}\right) + C$$ $$= \arctan(r) + C$$

The final answer is $\boxed{\arctan(r) + C}$.