1. **State the problem:** Calculate the integral $$\int 1 \, dx$$. 2. **Formula used:** The integral of a constant $c$ with respect to $x$ is given by $$\int c \, dx = cx + C$$ where $C$ is the constant of integration. 3. **Apply the formula:** Here, $c = 1$, so $$\int 1 \, dx = 1 \cdot x + C = x + C$$. 4. **Explanation:** Integrating a constant means finding the area under a constant function, which is a straight line with slope zero. The result is the constant multiplied by the variable plus an arbitrary constant $C$ because integration is indefinite. **Final answer:** $$\int 1 \, dx = x + C$$