Answer
First we know that,
$$
\begin{aligned}
\left.\cos x \leq 1 \quad\left[ \text { multiply both sides by } e^{x} \right] \\
e^{x} \cos x \leq e^{x} \quad\left[ \text { integer both sides from o to 1} \right] \\
\int_{0}^{1} e^{x} \cos x d x \leq \int_{0}^{1} e^{x} d x =e^{x}\right]_{0}^{1}=e-1
\end{aligned}
$$
Therefore,,
$$
\int_{0}^{1} e^{x} \cos x d x \leq e-1
$$
Work Step by Step
First we know that,
$$
\begin{aligned}
\left.\cos x \leq 1 \quad\left[ \text { multiply both sides by } e^{x} \right] \\
e^{x} \cos x \leq e^{x} \quad\left[ \text { integer both sides from o to 1} \right] \\
\int_{0}^{1} e^{x} \cos x d x \leq \int_{0}^{1} e^{x} d x =e^{x}\right]_{0}^{1}=e-1
\end{aligned}
$$
Therefore,,
$$
\int_{0}^{1} e^{x} \cos x d x \leq e-1
$$
