Let \( R \) be the interior region between the lines \( 3x-y+1=0 \) and \( x+2y-5=0 \) containing the origin. The set of all values of \( a \), for which the points \( (a^2,a+1) \) lie in \( R \), is:
\( (-3,-1)\cup\left(\displaystyle\frac{1}{3},1\right] \)
\( (-3,-1)\cup\left(\displaystyle-\frac{1}{3},1\right] \)
\( (-3,0)\cup\left(\displaystyle\frac{2}{3},1\right] \)
\( (-3,0)\cup\left(\displaystyle\frac{1}{3},1\right] \)
