Question

What is the antiderivative of `-sinx dx`?

Answer 1

Let I = `int -sinx.dx`
I = `-int sinx.dx`
I = `- (-cos x)`

(Since `d/dx (cosx)= -sinx`,
`-d/dx (cosx) = sinx`)

Thus, I = cos x

Note that if you remember `d/dx (cosx)= -sinx`, you can directly get the answer since the antiderivative (integral) of a derivative is nothing but the function which was differentiated.