Find the volume of a solid formed by region R which is bounded by y = 1/(x^2+1) and y = -cos(x) and rotated about the line y = -2.

To find the volume of the solid formed by rotating region R about the line y = -2, we can use the method of cylindrical shells.

First, let's draw a graph of the two curves to visualize the region R:

```
y = 1/(x^2 + 1)
y = -cos(x)
```

The intersection points of these two curves will determine the boundaries of region R. Let's find those points:

```
1/(x^2 + 1) = -cos(x)
```

Let's solve this equation numerically. Here's how you can do it:

1. Choose an interval (e.g., [-5, 5]) that contains potential intersection points.
2. Divide the interval into smaller increments (e.g., 0.1) and evaluate both equations at each increment.
3. When the two equations have opposite signs at an increment, it indicates an intersection point.

Once you find the intersection points, you can determine the boundaries of region R.

After obtaining the intersection points, you need to determine which curve is above the other within region R. This will determine the upper and lower curves when finding the volume.

Now we can calculate the volume using cylindrical shells. The volume of each shell is given by the formula:

```
dV = 2πrh*dx
```

Where:
- dV: volume of the shell
- r: radius of the shell (distance from rotation axis to the curve)
- h: height of the shell (difference between upper and lower curves)
- dx: small width of each shell

Integrate the volume of all the shells within the boundaries of region R to find the total volume of the solid:

```
V = ∫(2πrh)dx
```

To evaluate this integral, you need to express r and h in terms of the x-coordinate.

After integrating, you will have the volume of the solid formed by rotating region R about the line y = -2.