f(x)=Integral of -(4n-7)x^n)/(6n+7) find f'(x)

Hello! I suppose that the variable of integration is x. Because the limits of integration are not given, I suppose we are speaking about the indefinite integral, which is also called the antiderivative.
This name reflects the fact that if we integrate a function g from any fixed point a to x, then the derivative of this integral will be g(x) again:
d/(dx) (int_a^x g ( t ) dt) = g(x).
It is the so-called Fundamental Theorem of Calculus. Therefore, the derivative of our indefinite integral is the integrand, i.e., the function
-(4n - 7) / (6n + 7) x^n.
This is the answer. If you are interested in the integral itself, it is also simple if we suppose n is independent of x:
int-(4n - 7) / (6n + 7) x^n dx =-(4n - 7) / (6n + 7) int x^n dx =-(4n - 7) / ((6n + 7)(n+1)) x^(n+1) + C
for n != -1, and -(4n - 7) / ((6n + 7)(n+1)) ln|x| + C for n = -1.
Here, C is an arbitrary constant.
http://tutorial.math.lamar.edu/Classes/CalcI/IndefiniteIntegrals.aspx