How to open a shell command prompt inside Visual Studio Code?

Use CMD+Shift+C or CTRL+Shift+C but it will only open a new outside editor standard bash console.

I hope they will implement an integrated console.

For integrated console use Ctrl+`

From the release notes:

With the May release, we are rolling out the initial version of an integrated terminal. You can open the terminal using Ctrl+`, from the View | Toggle Integrated Terminal menu, or from the View > Toggle Integrated Terminal command in the Command Palette.

https://code.visualstudio.com/updates#_workbench