Hello Bettina, "make up one's mind" is an idiom and it means "decide what o do or choose between alternatives." * Maybe Paris, maybe Canada. He can't make up his mind yet*. So the correct form used in that idiom would be :" I can't make up my mind". Yet "make up" as a phrasal verb has got other meanings such as : -fabricate ,manufacture -compensate, even off -catch up with -settle In case of other senses you might separate 'make' and 'up' .

In my opinion both are now considered grammatically correct. However, some people still believe that it is incorrect to end a sentence with a preposition like "up". So when you are writing you should take into account that some people still believe that it is more correct to write--- I can't make up my mind-------- :)

You can say both! They are both perfectly correct!