How to repair a fault in roof
This problem is likely caused by one of these things:


The wood roof sheathing under the sag area is rotted away eliminating the support for the shingles. 
There is a gap between the sheathing edge and the rain gutter with no support for the shingles. Over time with heat and freezing cycles and winter ice build up the shingles has just sagged into the gap.
The rain gutter was installed too high on the rafter end fascia and it pushed up the tails on the lower course of shingles.


The fix needed to take care of the problem will require detailed analysis to determine the exact cause of the dished shingles. Once that is understood you can proceed with the proper fix.