I prefer #2, but both are correct. The first can be seen as: I would like to apply what I learned in school ( in order ) to help people.
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Seraphin"I would like to apply what I learned in school to help people" ?You have two place holders here: 1) the activity to which something is applied: ---ing, and 2) the purpose for which
"I would like to apply what I learned in school to helping people" ?