I'm asked to state the fundamental theorem of calculus, and use it to show that

d/dx

integral from x to tan x$\displaystyle \frac{1}{1+t^{2}}=\frac{x^{2}}{1+x^{2}}$.

I've been trying to use the wikipedia definition:

Fundamental theorem of calculus - Wikipedia, the free encyclopedia

So I have f(t)=1/(1+t^2)

a = x, b= tan x

But what do I use for the F(x)?

Or is one supposed to use some corrollary?

And to 'show something using the Fun. Theorem of Caculus', does one simply say: "Thus, by the Fundamental Theorem of Calculus.. qed."?