The question is:
How many calories are required to convert 17g of ice at 0.0 Celsius to liquid water at 32.0 Celsius?
I used Heat=Mass x Change in Temp x Specific Heat and got the answer 544 calories over grams Celsius.
Is this correct?

You are not accounting for the heat needed to melt the ice (heat of fusion of water).
Check your book for that and you will get the right answer.

Thanks! Thank you!