Question

Thanks for helping with calculus

Answer 1

Integrating
`f(x)` gives

`g(x)=\displaystyle\int f(x)\,\mathrm dx=C+\sum_(n=0)^\infty(a_n)/(n+1)x^(n+1)`

Notice that
`x=0` forces all terms in the sum to be 0, so that

`g(0)=C=5`

and hence

`g(x)=\displaystyle5+\sum_(n=0)^\infty(a_n)/(n+1)x^(n+1)`

making the first option correct.