Actually to make something connected, it should have more than $\frac{(n-1)(n-2)}{2}$ edges, i.e, just add one more edge. This gives $\frac{n^{2} - 3n + 4}{2}$ edges
Now here in 2nd option,
$C(m,2) -m + 2$ (n is replaced by m)
This also gives $\frac{n^{2} - 3n + 4}{2}$ edges.
Now, I am not getting the options :P