Final answer:
A transmembrane protein first gets inserted into the Endoplasmic Reticulum, processed in the Golgi apparatus, and then directed to the plasma membrane where it becomes an integral part.
Step-by-step explanation:
A transmembrane protein destined for the plasma membrane will first be inserted into the Endoplasmic Reticulum (ER). The rough ER, which is studded with ribosomes and continuous with the nuclear envelope, synthesizes membrane and secretory proteins. These proteins, like the transmembrane proteins, remain bound to the membrane of the rough ER and are later packed into transport vesicles. These vesicles then fuse with the cis face of the Golgi apparatus, where the proteins are further modified and then sorted to their final destinations, including the plasma membrane.
After processing in the Golgi apparatus, the proteins are packaged into vesicles that bud off from the Golgi's trans face. Eventually, when these vesicles fuse with the plasma membrane, the transmembrane protein becomes an integral part of it.