The answer is the third one (or C): closing the project.
Explanation for each option:
a. Monitoring and controlling the project work: This phase involves tracking, reviewing, and regulating the progress and performance of the project. It ensures that the project stays on track and meets its objectives. However, this does not involve gathering final project records or archiving information.
b. Integrating the project plan: This refers to the coordination of various elements of the project plan to ensure they work together effectively. It is more about the planning and execution phases rather than the final stages of the project.
c. Closing the project: This phase involves finalizing all project activities, gathering project records, analyzing the project's success, collecting lessons learned, and archiving project information. These activities match the description given in the question.
d. Managing project execution: This phase involves carrying out the project plan by performing the activities included in it. It focuses on the actual work being done to produce the project's deliverables, not on finalizing and closing the project.
Summary:
The activities described in the question—gathering project records, analyzing the project's success, collecting lessons learned, and archiving project information—are all part of the project closure phase. Therefore, the correct answer is C: closing the project.