1. **Problem Statement:** Calculate the integral $\int x^2 \, dx$. 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. **Applying the formula:** Here, $n=2$, so $$\int x^2 \, dx = \frac{x^{2+1}}{2+1} + C = \frac{x^3}{3} + C$$ 4. **Explanation:** We increase the exponent by 1 and divide by the new exponent. This reverses the differentiation power rule. 5. **Final answer:** $$\int x^2 \, dx = \frac{x^3}{3} + C$$