$\displaystyle \int_0^2 \frac{(x+1)^2}{x^{2}+1} dx$
ok ive got to $\displaystyle \int_0^2 1.dx +\int_0^2 \frac{2x.dx}{x^{2}+1} $and got really confused what happens to the limits when you use change of variable say $\displaystyle t=x^{2}+1 $
$\displaystyle \int_0^2 \frac{(x+1)^2}{x^{2}+1} dx$
ok ive got to $\displaystyle \int_0^2 1.dx +\int_0^2 \frac{2x.dx}{x^{2}+1} $and got really confused what happens to the limits when you use change of variable say $\displaystyle t=x^{2}+1 $
If you can see that the derivative of $\displaystyle x^2 + 1$ is $\displaystyle 2x$, you don't need to change your limits. However, if you really want to change it, remember that the limits are just values for x. So:
because
$\displaystyle t = x^2 + 1$
when $\displaystyle x = 0, t = 1$
when $\displaystyle x = 2, t = 5$