Find $F'(x)$ given $ \int_x^{x+2} (4t+1) \ \mathrm{dt}$ Given the problem find $F'(x)$:
$$ \int_x^{x+2} (4t+1) \  \mathrm{dt}$$
I just feel stuck and don't know where to go with this, we learned the second fundamental theorem of calculus today but i don't know where to plug it in. What i did:


*

*chain rule doesn't really take into effect here(*1) so just replace t with $x$

*$F'(x) = 4x + 1$


though the answer is just 8, what am i doing wrong?

The second fundamental theorem lets you differentiate $\int_k^x f(t)\,dt$ with respect to $x$ where $k$ is  a constant. Note that there's only one $x$ in the limits of the integral here. 
Can you rewrite your integral as a difference of two integrals, each with just one $x$ in the limits of integration? Then you can try to apply the second fundamental theorem to each one.
