For context, this is the first math class in Bachelor's electrical engineering.
Our teacher has just given us a definition for the area under a curve as the following:
If $f(x)$ is an integrable and non-negative function on a closed interval $[a, b]$, then the area under the curve $y = f(x)$ in that range is the integral of $f(x)$ evaluated from $a$ to $b$.
I asked him why the non-negative condition is given, and we're a little stuck trying to find an answer.
In a real-life context, I understand that areas are negative. But when applied to stuff like physics, we'll have to account for the sign as it often denotes ideas like direction. Moreover, imo pure mathematics should allow for negative areas.
Does anyone have any answers?