This is one common definition of the term history, but it's not a very good one and largely relegated to outdated encyclopedia entries rather than describing how professionals investigate history. It's very poor as a technical definition. For instance, does "history" in an area start when someone writes something, or does the writing have to survive to the present day? Does only one person need to write, or does it need to be socially widespread? Does it have to be full writing or does protowriting count? Do we have to be able to read the writing? Do partial readings count? These ambiguities weren't issues back when it was being used as a criterion for "civilization" ala childe, but that time has long since passed.
Today, it's best to ignore all these difficult and largely unnecessary questions by simply using a descriptive definition where "history is the human past".