1. **State the problem:** Evaluate the integral $$\int (3x^2 - 4x + 5) \, dx$$. 2. **Recall the formula:** The integral of a power function $$x^n$$ is given by $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ where $$C$$ is the constant of integration. 3. **Apply the integral to each term:** - For $$3x^2$$, $$\int 3x^2 \, dx = 3 \int x^2 \, dx = 3 \cdot \frac{x^{3}}{3} = x^3$$. - For $$-4x$$, $$\int -4x \, dx = -4 \int x \, dx = -4 \cdot \frac{x^{2}}{2} = -2x^2$$. - For $$5$$, $$\int 5 \, dx = 5x$$. 4. **Combine all results:** $$\int (3x^2 - 4x + 5) \, dx = x^3 - 2x^2 + 5x + C$$. 5. **Final answer:** $$\boxed{x^3 - 2x^2 + 5x + C}$$