The integral presented in the image is $\int x^2 \, dx$.

To solve this, we use the power rule of integration, which states:

$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$

where $C$ is the constant of integration.

Applying this rule to our integral:

$\int x^2 \, dx = \frac{x^{2+1}}{2+1} + C = \frac{x^3}{3} + C$

Therefore, the solution is:

$\frac{x^3}{3} + C$

Would you like more details or have any questions?

Here are five questions you might want to explore next:

1. How do you integrate $\int x^3 \, dx$?
2. What is the integral of $\int e^x \, dx$?
3. Can you explain the substitution method for integrals?
4. How do you find the area under a curve using integration?
5. What are definite and indefinite integrals?

Tip: Remember, the power rule for integration is a fundamental tool in calculus, and understanding it thoroughly will help you solve a wide range of integral problems.