I have encountered the same question,too. There are many occasions where you may want to record within a customized region on your PC. It can not only protect your desktop privacy, but also focus what you are trying to present. As you mentioned above, it is difficult to find proper recording software among plenty of programs, you may even find some apps are fraud and mess you up. No worries, here I’ll show you two ways to capture part of screen for free, you can try both of them and find which is better.
Way1: Apowersoft Free Online Screen Recorder
It’s an awesome screen recorder which supports to record specified area videos so that the rest of your computer screen aren’t showing on the recording, you can use it to record desktop activities, menus and cursor actions. Moreover, it provides two modes include Region and Around mouse to record part of screen, and you can drag the mouse to select recording area according to your requirements.

User guides to record customized area with Apowersoft Free Online Screen Recorder
Now let me show you the detailed steps to capture selected area of screen
Step1: Enter the website and click Staring Recording button
Step2: Launch the program and make some settings, click Options button under Tools menu, it will pop up a dialog box, you have the ability to choose your favorite hotkeys.
Step3:When everything is ready, just click Start button and drag pull-down list to choose Region or Around mouse to record section of screen.
Tips: Before recording, you are able to choose different resolutions to satisfy your needs. If you want to record HD videos, you should choose the resolution of 1080p or 720p.
It is easy to capture onscreen activities with this tool, a detailed demo video is provided to teach you.
Way2: Camstudio
As far as I know, Camstudio is a professional screen video recorder that allows you to capture a particular region for free. It provides various modes for you to choose from: Region, Fixed Region and Window. If you choose Fixed Region under Region menu, you will be able to enter parameters indicating the position and the size of desired screen recording area, which is a distinctive feature compared with Apowersoft Free Online Screen Recorder.

Although it’s great for capturing part of screen in different modes, it still has some disadvantages in using it. For instance, lots of users reflected that all they can see was a black screen with audio when replayed the output video. Besides, the interface isn’t intuitive, so it may be complicated to operate it for a green hand.
With both programs, you can capture any area of desktop without a buck. But in this case what you need is a tool that enables you to capture portion of screen instantly, I think Apowersoft Free Online Screen Recorder is more suitable for you, it is much easier to handle compared with Camstudio. If you still have any doubts, please feel free to leave a comment.