Match List-I with List-II

List-I	List-II
Definite integral	Value
(A) $\int_2^3 x^2 dx$	(I) $-\frac{1}{2}$
(B) $\int_{-1}^1 (x+1)dx$	(II) $\frac{19}{3}$
(C) $\int_0^1 (x-1)dx$	(III) $\frac{16}{3}$
(D) $\int_0^4 \sqrt{x}\,dx$	(IV) 2

Choose the correct answer from the options given below:

If $\int e^{3\log x}(x^4+1)^{-1}dx = \frac{m}{n}\log(x^4+1)+C$, where C is an arbitrary constant, $m$ and $n$ are positive integers such that g.c.d $(m,n)=1$, then $(4m^2+n^2)$ is equal to

The value of integral $\int_{-\pi/2}^{\pi/2} \frac{1}{1+e^{\sin x}}dx$ is

If $\int \frac{2x - 5}{(2x - 3)^3} e^{2x} dx = \frac{\lambda e^{2x}}{(2x - 3)^2} + C$, where $C$ is an arbitrary constant then the value of $\lambda$ is

The value of the integral $I = \int_0^1 \frac{1}{\sqrt{x^2 + 2x + 3}} dx$ is:

$\int \dfrac{e^{7\log x}-e^{6\log x}}{e^{5\log x}-e^{4\log x}}\,dx$, $x>0$ and $x\ne 1$ is equal to (consider $\log x = \log_e x$)

The value of $\int_0^{\pi/2} \log_e \left(\frac{5 + 2 \sin x}{5 + 2 \cos x}\right) dx$ is