Question

What is `f(x) = int x^2+x-3` if `f(2)=3`?

Answer 1

I found: `f(x)=x^3/3+x^2/2-3x+13/3`

Explanation:

We solve the indefinite integral:
`int(x^2+x-3)dx=x^3/3+x^2/2-3x+c`
and then we use our condition to find `c`:
`f(2)=3=(2^3)/3+(2^2)/2-(3*2)+c`
so:
`3=8/3+4/2-6+c`
`c=3-8/3-2+6`
`c=7-8/3=(21-8)/3=13/3`
and finaly:
`f(x)=x^3/3+x^2/2-3x+13/3`