Samsung has the habit of fiddling quite a lot with Android and what you call 'the Internet browser' is probably a version of the stock android browser that Samsung then have fiddled with. There may an option to clear the browser data manually.
Alternatively, Firefox for Android has the option to do this automatically every time you close it. You can also select which data is cleared (browsing history, cache, search history, cookies and so on).
There are likely other browsers with the same options.