I can't find a working solution to get to the integral of

$\displaystyle f(x)=\frac{2}{3}x+3$

Because the answer is given in the solutions as

$\displaystyle F(x)=\frac{1}{3}x^{2}+3x+c$

I can work backwards easily enough to see that it is correct.

But without the solution I can't figure it out for myself.

Can anybody explain to me how I would do this on my own?

Many thanks.