Maria, who has a thing for numbers, was all excited. "Hey, what are you so excited about?" asked Fred. "I just proved that

$\displaystyle \int _{0}^{\pi }\!\sin \left( {x}^{2} \right) {dx}

$

is a rational number," said Maria. "No way, that couldn't possibly be a rational number," said Fred. "Not only is it rational but it equals

$\displaystyle {\frac {4616282458010182669}{5974596810169649399}}$

which is a ratio of two prime numbers," said Maria excitedly.

Who is right?

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Note: I only have a solution using Maple. This is a really dumb problem. Please don't waste a lot of time on it.