Hey,
I hope this helps, I integrated your function.
Integrate (-1/16x^2 +1), from -4,4. = -1/48x^3+x, from -4, 4.
So. [(-1/48)(4^3)+4]-[(-1/48)(-4^3) - 4]
= [-4/3 +4 ] - [4/3 -4]
= 8-(8/3)
= 16/3
This should give you the area under the graph from -4 --> 4
hope this works...