1. Given $x \in \mathbf{R}$, and $x \neq \frac{k \pi}{2}(k \in \mathbf{Z})$. Then $M=$ $4^{\sin ^{2} x}+4^{\cos ^{2} x}$ the integer part is ( ).
(A) 4
(B) 5
(C) 6
(D) 8
1. A.
On the one hand,
$$
M \geqslant 2 \sqrt{4^{\sin ^{2} x} \times 4^{\cos ^{2} x}}=2 \sqrt{4^{\sin ^{2} x+\cos ^{2} x}}=4.
$$

On the other hand, since $0<\sin ^{2} x<1$, then $1<4^{\sin ^{2} x}<4$, hence
$$
\left(4^{\sin ^{2} x}-1\right)\left(4^{\sin ^{2} x}-4\right)<0,
$$

which means $\left(4^{\sin ^{2} x}\right)^{2}+4<5 \times 4^{\sin ^{2} x}$.
Dividing both sides by $4^{\sin ^{2} x}$, we get
$$
4^{\sin ^{2} x}+4^{1-\sin ^{2} x}<5,
$$

which is $4^{\sin ^{2} x}+4^{\cos ^{2} x}<5$.
Therefore, $4 \leqslant m<5$. Hence, the integer part of $M$ is 4.