Razor 9DOF SMD Capacitor replacing
You are on a tough road. I hope someone can give you specifics.  Normally you would able to identify the capacitor from its parts designation, but that board does not have any. So you will have to match the schematic (assuming spark fun provides one) to the board layout to figure out what it is.  The cost of the part is probably over a penny, maybe even 2 cents. In other words, not an issue.

It will require hot air to desolder one from another board and to solder this one on. Someone might be able to do it with a fine tip solder  pencil, but not likely.

Bottom line; find someone who has experience repairing boards, or order another one. Amazon has breakout boards for the 6050 for $6. But I see this one has Serial, and a magnetometer, so it is not quite the same. But depending on what you plan to do with it, it could work.