2D integrating cells provide long optical path lengths on a chip by multiple reflections at highly reflective mirrors similar to integrating spheres in free space. Therefore, they build a promising platform for integrated optical absorption sensing. Here, we present first absorption measurements of free carriers generated by a modulated pump laser inside a 2D integrating cell in a silicon slab. The results can be used to evaluate the lifetimes of free carriers in silicon slabs for integrated optics. Employing a silicon-on-insulator platform with a silicon thickness of 220 nm, we demonstrate measurements of the access free-carrier concentration on the order of 1-8·1015 cm-3 with lifetimes on the order of 0.1-1 μs governed by surface recombination at the silicon interfaces. The measured lifetimes are dependent on free-carrier concentration, which confirms previous observations. The presented free-carrier absorption experiment verifies the sensitivity of 2D integrating cells to changes in the absorption coefficient and thus demonstrates the potential of 2D integrating cells for absorption sensing.