The first step for this problem is to integrate the expression (i.e. find the antiderivative). This will give us the expression for `y`.

`int(3x^2-2x)dx=x^3-x^2+K`

So we have `y = x^3− x^2+ K`

This represents a family of curves, and depends on the value of `K` for the y-intercept.

We must now find the value of `K` from the information given in the question.

Since the curve passes through `(2, 5)`, we substitute these values into

`y = x^3− x^2+ K`

to give:

`5 = (2)^3 − (2)^2 + K`

`5 = 8 − 4 + K`

So `K = 1`.

So the required curve is `y = x^3− x^2+ 1`

Please support IntMath!