Let's definite the function f(x)=∫（from x to x+1）sin(t^2)dt
There is another function of x:
The Attempt at a Solution
Prove that when x→+∞，there is the equation:
Here the O(u) means that when u→0, the O(u) is at least infinite small comparable to the infinite small quantity u.
I am only a 12 grade highschool student, so I have no methods to solve this. I will be grateful if you could give me some advice. This is a problem from the exercises of the Mathematical Analysis by V.A.Zorich, chapter 6, Volume I.