THIS SAME EXACT THING HAPPENED TO MINE!!!
mine looks basically the same as yours did in the picture. I called up Nintendo, I had my DS for a little over a year, and because the warranty is only for a year, they said they had to charge me.
They said it would be $75 + $7.50 for their UPS delivery service. So yeah, for a system I bought brand new for $130, they want $82.50 TO FIX PLASTIC!!! 63%.
Check out this site:
http://www.oldschoolgamer.ca/information.aspx?SID=29
I'll probably look for others, but this one has repairs starting at $40, which is still crazy considering it's plastic, but not as bad as Nintendo by any means. At this rate though, I think i'm gonna ask one of my more handy relatives on what I should do, probably take my chances with superglue.
Let me know how this goes and I'll be checking this too