I wonder if Quantum computer could be used to solve hard math problems like Integrals.

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Normal computers can't???
Well, first of all, through linear algebra all things are ~~solvable~~ approximal. So jot that down
It's hardly related, but I once had a nightmare that I was back to high school and had to take an exam on integrals, but since I didn't know anything I just repeated to the teacher (who strangely was my college teacher) that I was an arts student.

When I woke up, I asked my friends who were studying engineering what integrals were, none of them gave me a satisfactory answer, so to this day I still have no idea what they are.
- Very simply:
  
  A function defines a curve.
  
  A derivative reveals the slope of that curve at a very specific point.
  
  An integral reveals the area "under" the curve (the space bounded by the curve and the horizontal axis).
  
  Well yeah in the simple case.
  
  And then there's stochastics.