To solve the integral $\int \left(\frac{\pi}{4} - \frac{x}{2}\right) \, dx$, we can integrate each term separately.

1. Integrate $\frac{\pi}{4}$: $\int \frac{\pi}{4} \, dx = \frac{\pi}{4} x$

2. Integrate $-\frac{x}{2}$: $\int -\frac{x}{2} \, dx = -\frac{1}{2} \cdot \frac{x^2}{2} = -\frac{x^2}{4}$

Now, combining these results gives: $\int \left(\frac{\pi}{4} - \frac{x}{2}\right) \, dx = \frac{\pi}{4} x - \frac{x^2}{4} + C$

where $C$ is the constant of integration.

Thus, the final result is: $\frac{\pi}{4} x - \frac{x^2}{4} + C$

Would you like further details on this integration process or have any questions? Here are some related questions you might consider:

1. What are the applications of definite integrals?
2. How do you evaluate a definite integral?
3. What is the geometric interpretation of an integral?
4. Can you explain the Fundamental Theorem of Calculus?
5. What techniques can be used for integrating more complex functions?

Tip: When integrating, always remember to add the constant of integration $C$ since the integral represents a family of functions.