1. **State the problem:** Calculate the integral of a function, but since the function is not specified, let's consider a general example: find $\int x^2 \, dx$. 2. **Formula used:** The power rule for integration states that for any real number $n \neq -1$, $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ where $C$ is the constant of integration. 3. **Apply the formula:** For $n=2$, $$\int x^2 \, dx = \frac{x^{2+1}}{2+1} + C = \frac{x^3}{3} + C$$ 4. **Explanation:** We increase the exponent by 1 and divide by the new exponent. The constant $C$ accounts for any constant term that disappears upon differentiation. 5. **Final answer:** $$\int x^2 \, dx = \frac{x^3}{3} + C$$