Calculus college problem

Can you please share your work, step-by-step, using Liebniz integral rule?

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I just realized that the integral is by x which is not related to s and t, so if I'm understanding correctly, the formula doesn't work here.
In my answer I got zero from the 2nd subtraction and 3rd addition so it left me with the first part, but now I see that it's incorrect.
 
Thank you for your time, apparently my answer was right so the lecturer gave me back the point
 
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