Hello,

I am reading a calculus book and I am stuck with the following exercise:

Show if $\displaystyle \lim_{t\rightarrow\infty}\int_1^t \sin(x^2) dx$ is convergent or not.

Sadly, the solutions at the end of the book only say that it is convergent but don't give any hint on how to show this. I would appreciate any ideas as I have spent quite some time on it already and it nags me a bit. Thanks in advance.