# Net Area with Integration Question

Should be a fairly quick question, but I was given the following graph of $$g(x)$$:

which was followed by the question:

Let $$h(x)=\int_{-4}^xg(x)\,dx$$. On what open intervals contained in $$-4\le x\le11$$ is the graph of $$h$$ concave down? Give a reason for your answer.

So I'm a bit confused on how I'd find the values of $$h(x)$$, I'm assuming I just determine the respective integral for the specific value of $$x$$, like if I wanted to find $$h(2)$$ I'd plug 2 into the integral attached to $$g(x)$$ and I know that concavity is determined from the second derivative, but I'm extremely confused on how I'd go about finding the values of $$h''(x)$$. Any help is appreciated!

• Is that graph of $g(x)$? – Parcly Taxel Apr 25 '20 at 1:22
• Yeah, I forgot to include that, I'll put it in – joe Apr 25 '20 at 1:29

$$h(x)$$ is concave down at $$x$$ iff $$h'(x)=g(x)$$ is decreasing at $$x$$. We see that $$g(x)$$ is decreasing on $$(1,4),(4,6)$$ and $$(8,11)$$, so these are the same intervals on which $$h(x)$$ is concave down.