Both statement I and statement II in the question are individually true. Statement I states that after cutting an apple or a banana, the color of the cut surface becomes brown, which is a commonly observed phenomenon. Statement II explains that polyphenolic compounds present in fruits get oxidized in air and show color. This is also true because polyphenolic compounds in fruits, such as apples and bananas, are known to undergo oxidation reactions when exposed to air, which results in the brown color of the cut surface. Therefore, statement II provides a correct explanation for statement I.

Option 1, which states that both statements are individually true and statement II is the correct explanation of statement I, is the correct answer. The other options are incorrect because they either state that one of the statements is false (option 3) or that statement II is not the correct explanation (option 2) or that statement I is false (option 4), which is not the case.