I actually spoke to my local upholstery shop (same one who did my arm rest) about taking it in for an estimate to do that but never went

 

BTW OP since Its ur post here's a suggestion... I used 3M super 77 multi purpose adhesive and it worked great. What u can try doing is spraying some into a small container, brushing it onto both surfaces, letting it dry for a few mins (till its tacky) before putting it back on and then use a flat tool or cooking spatula too push the material back in the creases

 

if ya got the money, have someone do it...
in the end it looks better. if not, they can always re-do it

 

Some vinyl material that has the look and feel of leather. Pretty stretchy so very easy to use

 

+1 for 3M adhesive spray. Otherwise I'd take it to a shop.