Evaluate the following integral:
${\int }_1^4(2x+1)dx$

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.                                                                          

                                                                                                                                                                                     (b) Suppose ƒ is a negative increasing function, for 𝓍 > 0 . Then the area function A(𝓍) = ∫₀ˣ ƒ(t) dt is a decreasing function of 𝓍 .

Given the definite integral $F\left(x\right)={\int }_3^x[t^8-\sin \left(t^4\right)]dt$ , find the derivative $F^{\prime }\left(x\right)$.

Given the definite integral $F\left(x\right)=\int_{12}^{20x}\!\left(h^4+\frac{63h}{\sqrt{h^5}}\right)\,dh$, find the derivative $F^{\prime}\left(x\right)$.

Evaluate the following integral:

${\int }_0^{3}4dx$

Evaluate the following integral:

${\int }_{-1}^2(x^2-3x+2)dx$

Evaluate the following integral:

${\int }_0^1(2x^3-x^2+4x)dx$

Evaluate the following integral:

${\int }_2^3{x}^{\frac{5}{2}}dx$

Evaluate the following integral:

${\int }_1^2\frac{5}{x^2}dx$