1. **State the problem**: Find the integral of the polynomial function $$x^5 + 5x^2 - 6x + 7$$. 2. **Recall the integration rule**: The integral of $$x^n$$ with respect to $$x$$ is $$\frac{x^{n+1}}{n+1}$$ plus the constant of integration $$C$$. 3. **Apply the rule to each term**: - Integral of $$x^5$$ is $$\frac{x^{6}}{6}$$. - Integral of $$5x^2$$ is $$5 \times \frac{x^{3}}{3} = \frac{5x^{3}}{3}$$. - Integral of $$-6x$$ is $$-6 \times \frac{x^{2}}{2} = -3x^{2}$$. - Integral of $$7$$ is $$7x$$. 4. **Combine all integrals and add the constant**: $$\int (x^5 + 5x^2 - 6x + 7) dx = \frac{x^{6}}{6} + \frac{5x^{3}}{3} - 3x^{2} + 7x + C$$. This is the final answer.