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If the upper limit is a function of x and the lower limit is a constant, you can differentiate an integral using the Fudamental Theorem of Calculus. For example you can integrate Integral of [1,x^2] sin(t) dt as:
sin(x^2) d/dx (x^2)
= sin(x^2) (2x) = 2x sin(x^2)
The lower limit of integration is 1 ( a constant).
The upper limit of integration is a function of x, here x^2.
The function being integrated is sin(t)
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