This a pretty weird question... because:
But the limit: is undefined?
How am I meant to compute the MGF then?
I'm not familiar with what MGF stand for, but it looks like you may want to re-check your antiderivative step. I think there needs to be a negative in the exponent and a negative out front of everything; doing this, then evaluating the limit in k (assuming t>1) should give the correct result.
Does this help?