By definition of Fourier transform
$$X(\omega)=\int_{-\infty}^\infty x(t) e^{-j\omega t} dt $$
Now what will happen to the answer of transform for example in case of $x(t)= \cos(\omega_0 t)$ if limit is $0$ to $A$ instead of $-\infty$ to $\infty$?
For $x(t)=\cos(\omega_0 t)$ its fourier transform is given by $ X(\omega)= \pi[\delta(\omega-\omega_0) + \delta(\omega+\omega_o)]$
so if the limit is changed will it effect the answer?