Maybe the way to think about it is,

也许可以这样想
why do certain integrals

为什么某些积分
not depend on how you took the path, right?

不取决于你取什么样的路线
Let me ask you a different question.

让我问你们一个不同的问题
Forget about integrals.

先忘掉什么叫积分
You are on top of some hilly mountain.

你正站在某座小山的山顶
We have a starting point, you have an ending point, okay.

我们有一个起点和一个终点
I started the starting point, and I walked to the ending point.

我从起点出发走向终点
At every portion of my walk,

在我步行的每一段路中
I keep track of how many feet I'm climbing; that's like my △U.

我记录我爬的尺数这就好像我的 △U
I add them all up.

我把它们加起来
At the end of the day,

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