The negative sign became positive in the last step because of a change in the limits of integration. In the original expression, the integral is from $t = \frac{1}{4}$ to $t = 1$, with a negative sign in front. However, in the next step, the limits of integration are swapped to go from $t = 1$ to $t = \frac{1}{4}$.

Swapping the limits of an integral reverses its sign, effectively canceling out the original negative sign in front. Therefore, the negative sign becomes positive after changing the limits.

Would you like more details on this explanation, or have any other questions?

Here are some related questions:

1. How does changing integration limits affect the integral's sign in general?
2. Why is the property of reversing limits and negating the sign useful in calculus?
3. Can you explain other situations where such sign changes are used in integral manipulation?
4. What are some applications of this property in physics or engineering?
5. How does this technique simplify solving integrals in some cases?

Tip: When working with integrals, remember that reversing the limits changes the sign, which can be useful for simplification in complex expressions.