An AI models instantaneous prediction error rate is given by e$($t$)=0\mathrm{.}1$e$^0\mathrm{.}2$t $,$ where t is the number of epochs $($training cycles$).$ The team wants to know the total error accumulated over the first $20$ epochs. Question: Set up and evaluate the integral to find the total error over $20$ epochs. Explain how this informs model evaluation and improvement. Create a short video presentation to exhibit your comprehension about the scenario and your proposed solution.