Question
Let $w'(t)=t-4$ the rate per month which Math Dragon grows in weight, if his initial weight was 2.718 tons, what was his weight after 1 year after when he was born?
I wasn't really sure what to do and I think that I'm supposed to do $\int_0^1w'(t)$ but I'm not really sure.
You have a unit problem because the units of weight change are per month, not per year. You are not given the weight unit for $w'$ so I would assume $w'$ is in tons per month. Your basic idea to integrate the weight change is a good one but you need to adjust the upper limit. I'm not sure what to make of the fact that the weight is negative at $t=2$ and for a region around it.