Let $F(x)=\int\limits_1^{x^2} \cos \sqrt{t} d t$
Statement-1: $F'(x)=\cos x$
Statement-2: If $f(x)=\int\limits_a^x \phi(t) d t$, then $f'(x)=\phi(x)$
Answer & explanation
Correct answer: option 4
$f(x)=\int\limits_1^{x^2} \cos \sqrt{t} d t$
$f(x)=\cos \sqrt{x^2}\frac{d}{dx}(x^2)-\cos\sqrt{1}\frac{d}{dx}(1)$
$=2x\cos x$ (Statement - 1 false)
$f(x)=\int\limits_a^{x}\phi(t)dt$
$⇒f'(x)=\phi(x)\frac{dx}{dx}-\phi(a)\frac{da}{dx}=\phi(x)-0=\phi(x)$ (Statement - 2 true)