Answer
$f(x)=\displaystyle \frac{1}{20}x^{5}+\sinh x-\frac{\sinh 2}{2}x+1$
Work Step by Step
$f''(t)=x^{3}+\sinh x$
Using the antiderivatives table,
$f'(x)=\displaystyle \frac{1}{4}x^{4}+\cosh x+C$
Using the antiderivatives table,
$f(x)=\displaystyle \frac{1}{4}\cdot\frac{1}{5}x^{5}+\sinh x+Cx+D$
$f(x)=\displaystyle \frac{1}{20}x^{5}+\sinh x+Cx+D$
$\left\{\begin{array}{llll}
f(0)=1 & \Rightarrow & D=1 & \\
& & & \\
f(2)=2.6 & \Rightarrow & & \frac{32}{20}+\sinh 2+2C+1=2.6\\
& & & 2C=-\sinh 2\\
& & & C= -\frac{\sinh 2}{2}
\end{array}\right.$
$f(x)=\displaystyle \frac{1}{20}x^{5}+\sinh x-\frac{\sinh 2}{2}x+1$
