1. Let's solve the integral problem: $ \int x^2 \, dx $. 2. The formula for integrating a power function $ x^n $ is: $$ \int x^n \, dx = \frac{x^{n+1}}{n+1} + C, \quad n \neq -1 $$ 3. Here, $ n = 2 $, so applying the formula: $$ \int x^2 \, dx = \frac{x^{2+1}}{2+1} + C = \frac{x^3}{3} + C $$ 4. This means the antiderivative of $ x^2 $ is $ \frac{x^3}{3} + C $, where $ C $ is the constant of integration. 5. Therefore, the final answer is: $$ \boxed{\frac{x^3}{3} + C} $$