Are there any restrictions using substitutions in integrals?

I'm trying to evaluate the following definite integral:

$\int_{0}^{1} \frac{x}{\sqrt{x+1}} dx$

Well I put the integral on symbolab to know its value ($4/3$)

However when I tried to calculate the integral using the substitution $x= t^2-1$ and making my new extremes of integration $1$ and $\sqrt 2$ I got to $\frac{4-2\sqrt 2}{3}$.

Well I wonder why... I verified on symbolab and the integral I calculated is correct. But the substitution gives my integral a different value.

Can someone explain me why? How can I make a correct substitution?

Thanks!

1 Answer

Symbolab's value is wrong. The integral is actually $\frac{4 - 2\sqrt{2}}{3},$ as you can check at wolframalpha