# Math Help - Graphing Integrals by hand

1. ## Graphing Integrals by hand

Hi, I was wondering how to sketch the graph of an integral. The function is:

f(x)=integral(lower limit 1 upper limit x) 2t/t^3+1

I was thinking that I could take the anti-derivative, but would that become the derivative f'(x) by FTC. Thanks for any help guys!

2. In general you have $\int_{a}^{x} f(t)dt = F(x)-F(a)$ by the fundamental theorem of calculus. This is a function which you can graph.
Now you must use the partial fraction theorem to get that $\frac{2t}{t^3+1} = -\frac{2}{3(t+1)}+\frac{2t+2}{3(t^2-t+1)}$