1. The problem is to find the integral of the function $y=\frac{1}{x^2+1}$.\n\n2. The formula for the integral of $\frac{1}{x^2+1}$ is a standard integral: $$\int \frac{1}{x^2+1} \, dx = \arctan(x) + C$$ where $C$ is the constant of integration.\n\n3. This formula comes from the fact that the derivative of $\arctan(x)$ is $\frac{1}{x^2+1}$.\n\n4. Therefore, the integral of $y=\frac{1}{x^2+1}$ is simply: $$\int y \, dx = \arctan(x) + C$$\n\n5. This means the area under the curve $y=\frac{1}{x^2+1}$ from any point to another can be found using the arctangent function.