Position, Velocity, Acceleration problem

A particle moves along the $\displaystyle x-axis$ so that at any time $\displaystyle t \geq 1$ its accelaration is given by $\displaystyle a(t)= \frac{1}{t}$. At $\displaystyle t=1$, the velocity of the particle is $\displaystyle v(1)=-2$ and its position is $\displaystyle x(1)=4$.

a) Find the velocity $\displaystyle v(t)$ for $\displaystyle t \geq 1$.

b) Find the position $\displaystyle x(t)$ for $\displaystyle t \geq 1$.

c) What is the position of the particle when it is farthest left?

I answered parts (a) and (b) (unsure if they're correct):

a) $\displaystyle v(t)=\ln {t}-2$

b) $\displaystyle x(t)=t\ln {t}-3t$

However I cannot answer part (c), here's what i have done(I have a bad feeling I am totally wrong):

$\displaystyle \int_1^\infty (\ln {t}-2) \, dt = \infty$

Can anyone help?

Thanks in advance!