1. The problem is to calculate the integral of a given function. Since the function is not specified, let's consider a general example: calculate the integral of $f(x) = x^2$. 2. The formula for the integral of a power function $x^n$ is: $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ where $C$ is the constant of integration. 3. Applying this formula to $f(x) = x^2$, we have: $$\int x^2 \, dx = \frac{x^{2+1}}{2+1} + C = \frac{x^3}{3} + C$$ 4. This means the antiderivative of $x^2$ is $\frac{x^3}{3} + C$. 5. In plain language, to integrate $x^2$, we increase the exponent by 1 (from 2 to 3) and divide by the new exponent (3), then add the constant $C$ because integration is indefinite. Final answer: $$\int x^2 \, dx = \frac{x^3}{3} + C$$