5.3 The Fundamental Theorem of Calculus/8

${\begin{aligned}g(x)=\int _{3}^{x}e^{t^{2}-t}dt\\\end{aligned}}$

${\begin{aligned}u&={\tfrac {1}{\sqrt {2}}}(x+y)\qquad &x&={\tfrac {1}{\sqrt {2}}}(u+v)\\[0.6ex]v&={\tfrac {1}{\sqrt {2}}}(x-y)\qquad &y&={\tfrac {1}{\sqrt {2}}}(u-v)\end{aligned}}$