Final answer:
The medication should be delivered in the hypodermis layer of the integument.
Step-by-step explanation:
The medication should be delivered in the hypodermis layer of the integument. The hypodermis is the layer of adipose (fat) tissue below the dermis, which is where subcutaneous injections are typically administered. These injections are given just below the surface of the skin, into the fatty layer of tissue, allowing for slow absorption of the medication into the bloodstream.