The first step for this problem is to integrate the expression (i.e. find the antiderivative).

So we have y = x³ − x² + 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 = x³ − x² + K

to give:

5 = (2)³ − (2)² + K

5 = 8 − 4 + K

So K = 1.

So the required curve is y = x³ − x² + 1.