In other words,

换言之
your job is to guess a function whose second derivative is a,

你的任务是要猜出一个二阶导数为a的函数
and this is called integration,

这就是积分
which is the opposite of differentiation,

和微分恰恰相反
and integration is just guessing.

积分就是猜
Integration is not an algorithmic process like differentiation.

积分不是微分那种演算过程
If I give you a function,

如果我给你一个函数
you know how to take the derivative.

你就知道如何求导
Change the independent variable, find the change in the function,

改变自变量算出函数的变量
take the ratio and that's the derivative.

计算比值这就是求导
The opposite is being asked here.

这里要求的是相反的过程
I tell you something about the second derivative of a function

我告诉你一个函数的二阶导数