Which of the following structures is integral to the movement in amoeba-like protists?

Pseudopodia are the structures that are integral to movement in amoeba-like protists. These are temporary projections of the cell's cytoplasm that extend and retract as the amoeba moves. By forming pseudopodia, these organisms can push their cytoplasm forward, enabling them to flow into new areas and effectively "crawl" across surfaces.

Pseudopodia not only facilitate movement but also assist in the process of phagocytosis, where the amoeba engulfs food or other particles. This adaptability allows them to explore their environment and encounter nutrients.

In contrast, cilia are hair-like structures that provide locomotion in many other protists but are not utilized by amoebae, which rely on their flexible, amoeboid movement. The pellicle is a layer that provides structural support but does not contribute directly to movement. Eyespots are sensory structures primarily related to detecting light and do not play a role in facilitating movement.