We have $\frac{dF}{dx}=f(x)$ $(x\in R)$
a)If $f(x)$ is periodic function then is $F(x)$ periodic too?
b)If $f(x)$ is odd function than is $F(x)$ even function?
My work.
a)$lim_{h\to 0}\frac{F(x+h)-F(x)}{h}=lim_{h\to 0}\frac{F(x+h+T)-F(x+T)}{h}$ how continue from here to proof that $F(x)=F(x+T)$?
b)$\frac{dF}{dx}=f(x)$ is odd
$-f(x)=f(-x)$
$f(-x)= $ $lim_{h\to 0}\frac{F(-x+h)-F(-x)}{h}=lim_{h\to 0} \frac{F(x)-F(x+h)}{h} $ and can't continue from here.