Let's consider the integral of the following equation:

$f(x) = 3x^2 - 5x + 4$

We want to find the integral of this function with respect to $x$:

$\int (3x^2 - 5x + 4) \, dx$

Steps to Solve:

1. Integrate each term separately:

   • The integral of $3x^2$ is $x^3$.
   • The integral of $-5x$ is $-\frac{5}{2}x^2$.
   • The integral of $4$ is $4x$.

2. Combine the results: $\int (3x^2 - 5x + 4) \, dx = x^3 - \frac{5}{2}x^2 + 4x + C$ where $C$ is the constant of integration.

Final Result:

$\int (3x^2 - 5x + 4) \, dx = x^3 - \frac{5}{2}x^2 + 4x + C$

Would you like more details on any specific part of this process, or do you have any questions? Here are some related questions you might consider:

1. How do you find the definite integral of this function over a specific interval?
2. What is the geometric interpretation of the integral in this case?
3. How can you apply integration to solve real-world problems?
4. What techniques can be used for integrating more complex functions?
5. Can you explain the concept of the constant of integration $C$?

Tip: When integrating, always double-check your work by differentiating your result to see if you obtain the original function.