Prove that there is a constant C such that

\(\displaystyle \sup_{A<B} \int_A^B \sin(x^2+ yx) \, dx \le C\)

for all y.

The  best solution was submitted by Minjae Park (박민재), KSA (한국과학영재학교)  3학년. Congratulations!

Here is his Solution of Problem 2010-13.

Alternative solutions were submitted by 정진명 (수리과학과 2007학번, +3), 정성구 (수리과학과 2007학번, +3), 심규석 (수리과학과 2007학번, +3). Three incorrect solutions were submitted (서**, 정**, Ver**).