To find the equation of the curve, we need to integrate the derivative \(\frac{dy}{dx} = -x^2 + 5x - 4\).

Integrating term by term, we have:

\(y = \int (-x^2 + 5x - 4) \, dx = \int -x^2 \, dx + \int 5x \, dx - \int 4 \, dx\).

This gives:

\(y = -\frac{x^3}{3} + \frac{5x^2}{2} - 4x + c\), where \(c\) is the constant of integration.

We use the point (6, 2) to find \(c\):

\(2 = -\frac{6^3}{3} + \frac{5 \times 6^2}{2} - 4 \times 6 + c\).

\(2 = -72 + 90 - 24 + c\).

\(2 = -6 + c\).

\(c = 8\).

Thus, the equation of the curve is \(y = -\frac{x^3}{3} + \frac{5x^2}{2} - 4x + 8\).