An object is heated in an oven and then taken out to cool. The function $y=A(t)$ represents the instantaneous rate of change of the temperature $($in degrees Celsius per minute$),$ where $t$ is the number of minutes after it was taken out. We know that the initial temperature was $550$ degrees Celsius.

Which expression below represents "the temperature after $15$ minutes"?

${\displaystyle \underset{0}{\overset{15}{}}}(A(t)+550)dt$

$550+A(15)$

$550+{\displaystyle \underset{0}{\overset{15}{}}}A(t)dt$

$A(15+550)$

$550-{\displaystyle \underset{0}{\overset{15}{}}}A(t)dt$

${\displaystyle \underset{0}{\overset{t}{}}}A(15)dt$

None of these

If ${\displaystyle \underset{0}{\overset{15}{}}}A(t)dt=-27$ and ${\displaystyle \underset{5}{\overset{15}{}}}A(t)dt=-26,$ then find each value below $($if possible$).$ If a value is not possible to find, write DNE as your answer.

"The change in temperature over the first $15$ minutes."

degrees Celsius

"The change in temperature over the first $5$ minutes."

degrees Celsius

"The object's temperature at $15$ minutes."

degrees Celsius