how can i solve by FTC?

$\displaystyle

\underset{x\to 0}{\mathop{\lim }}\,\frac {1}{x^{2}}\int_{0}^{x^{2}}{\frac {t + \sin ^{2}\sqrt {t}}{t + 1}}dt$

same condition for this one (use FTC)

find F'(x)

$\displaystyle

F\left( x \right) = \int_{0}^{x}{\ln \left( (tx)^{x} \right)}dt$

and this one too :roll:

find

$\displaystyle g''\left( x \right) + g\left( x \right)$

where

$\displaystyle

g\left( x \right) = \int_{0}^{x}{f(t)\sin (x)dt}

$