Answer
$F(1)-F(0)$
Work Step by Step
Step 1. Based on the Fundamental Theorem of Calculus, if $F(x)$ is an antiderivative of $f(x)$ on $[a,b]$, we have $\int_a^b f(x)dx=F(b)-F(a)$
Step 2. In the case of the exercise, we have $f(x)=\sqrt {1+x^4}$ and $F(x)$ is its antiderivative.
Thus, we have
$\int_0^1 f(x)dx=F(1)-F(0)$
(it seems that the antiderivative of $f(x)$ takes a complicated form, which is not required to solve by the exercise.)
