Question asks to find F(-1) and then F'(x) please explain thoroughly how u would solve this, thank you!

Question

f(x) = ∫ 1 to x^2 (as the x value range) sin(t) dt

Answer 1

f(x) = ∫_{(1 to x}2₎ sintdt

f(1) = ∫_{(1 to 1)} sintdt = 0

By the Fundamental Theorem of Calculus and the Chain Rule,

f'(x) = sin(x²)(x²)' = 2xsin(x²)