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The value of the definite integral 

\[
\int_{-1}^{4} (5x^4 - 8x^3 + 6)\, dx
\]

is 545.

Would you like more details or have any questions about the solution? Here are 5 related questions to expand your understanding:

1. How do we find the antiderivative of a polynomial function?
2. What is the process for solving definite integrals using limits of integration?
3. How does the Fundamental Theorem of Calculus apply to this problem?
4. Can this integral be solved using numerical methods? What are they?
5. How would the answer change if the limits of integration were different?

**Tip:** When solving integrals, always ensure that you correctly handle each term, including constants, before applying the limits of integration.

Evaluate the definite integral of (5x^4 - 8x^3 + 6) from -1 to 4.

Learn how to solve the definite integral of the polynomial function 5x^4 - 8x^3 + 6, evaluated from -1 to 4. This problem demonstrates key calculus concepts, including polynomial integration and the application of the Fundamental Theorem of Calculus.

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