The rumen is the first chamber in the stomach of ruminants such as cattle, sheep, and deer. Fermentation reactions by symbiotic organisms begin digesting plant matter in the rumen. If \( \mu \) is the fraction of matter entering or leaving the rumen per unit time in a model for continuous fermentation, then the integral
\[
\int_{0}^{1} \mu e^{-\mu t}(1-t) d t
\]
is the fraction of soluble material passing from the rumen in the first hour without being fermented. Evaluate this integral.