Final answer:
The unnecessary step when integrating a summary into a research paper is including supporting details from the source being summarized.
Step-by-step explanation:
When integrating a summary into a research paper, the step that is NOT necessary is to include supporting details from the source you are summarizing. This is because a summary should capture the main points or essence of the source material, rather than all the intricate details. This contrasts with the necessary steps like connecting the summary to your own ideas, correctly citing the source, and using a signal phrase to properly introduce the summary.