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enter image description hereLet $g$ be the function defined by

$$g(x) = \int_0^xf(t)dt$$

When $-4\leq x\leq6$

Graph $g$ using differentiation (check the monotonicity and concavity).

I tried applying the fundamental theorem of calculus with which I can conclude than the derivate of the given function is basically $x$. Is that the right approach or is there any other way to find the derivative of the function so that you can test it's monotonicity and concavity and sketch the required curve ?

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    I edited the question to make it more reasonable. In future, please use MathJax to format your questions. For a quick tutorial, see http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – 2017-02-17
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    Thanks! Is my approach to the question right? As if I were to infer from the equation that x is the derivative, then it only has one critical point ie 0 and no inflection points to test concavity which is why I'm confused as to whether I made an error. – 2017-02-17
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    Wrong, because the derivative is not $x$. – 2017-02-17
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    Sorry I added the graph to it – 2017-02-17

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The derivative of $g$ with regard to $x$ is not $x$, it is $f$. And without knowing what $f$ is, it is impossible to graph $g$, since $g$ can be any differentiable function you want.

I now see you added a picture of $f$. In this case, you know that $f$ is the derivative of $g$, so you can now know where $g$ is falling and where it is increasing. You can also easily calculate what $g(0)$ is equal to, and if you look at the derivative of $f$, you can get a view of the second derivative of $g$ is. That should be enough to sketch $g$.

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    Sorry, I added a graph to the given function is there any way to determine the function of the curve towards the right – 2017-02-17
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    @GaryAndrews30 I edited my answer. – 2017-02-17