Differentiate: ∫ x^2 to 1 ( t^(4) + 1 / t^(2) + 1 )dt

I dont get how after the step:

-d/dx ∫ 1 to x^2 ( t^(4) + 1 / t^(2) + 1 )dt

how you get to: -d/du ∫ 1 to u ( t^(4) + 1 / t^(2) + 1 )dt * du/dx.

How does using the chain rule affect the upper limit? I also dont really understand the notation, since I am very used to

f'(g(x))g'(x)