geometry - Arc length and area under curve

Hey guys I'm having trouble proving the area under the curve is the same as the arc length the question is:

$f(x)= \frac{1}{4}e^x+e^{-x}$ , prove that's the arc length on any interval has the same value as area under the curve.

For the arc length I got $\frac{1}{4}(e^x-4e^{-x})+C$. But I didn't get that for the area under the curve. Please help thank you !!