The problem is attached as a picture.
I believe the theories relevant to the equation are the Leibniz formula and the first or second fundamental theorem of calculus, I have two books and one lists the first theorem as the second and vice-versa. The theorem containing the derivative of the integral is the one I am looking at. The chain rule is also involved as well.
The Attempt at a Solution
I am stuck, my teacher explained how to do it today in class. I tried to integrate the function by reducing the power of sin(t^2) to (1/2)(1-cos2t) then differentiating that. I have no idea if that gives me correct answer as my teacher explained it an entirely different way using chain rule and fundamental theorem of calculus. When I check my answer and the answer I get from WolframAlpha by plugging in 1 after everything. They are very close but they are not the same, both answers were done in exact form, so no rounding issues.
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