How to copy one folder to another with existing files

For example,

/tmp/folder1
includes /tmp/folder1/a /tmp/folder1/b

/tmp/folder2
includes /tmp/c

Is there a command without removing files in /tmp/folder2 first to copy the /tmp/folder1 to /tmp/folder2?

and the result should be

/tmp/folder2 will include only /tmp/folder2/a /tmp/folder2/b

Assuming GNU cp (fileutils) you can do this:

cp -au $SOURCE/. $DEST/.

The -u option makes sure that existing and NEWER files are not overwritten.

sorry I meant

/tmp/folder2 will contain ONLY /tmp/folder2/a and /tmp/folder2/b