Let $h$ be the function defined by $h(x) = \int^{x^2}_0 e^{x+t} dt$ for all real numbers $x$. I've looked in Stewart and I've looked in Spivak. They both say to use the chain rule when evaluating something like this, which gives me h'(x) = e^{x+x^2} \cdot 2x, but apparently the true answer is h'(x) = (2x + 1) \cdot e^{x+x^2} - e^x.
Could somebody explain this?