Find the following integral, given that \[ \int_{a}^{b} f(x) d x=6 \text { and } \int_{a}^{b} g(t) d t=4 . \]

Step 1 ：Given that \(\int_{a}^{b} f(x) d x=6\) and \(\int_{a}^{b} g(t) d t=4\).

Step 2 ：We need to find the integral of the sum of the functions f(x) and g(t) from a to b. We can use the property of integrals that states the integral of the sum of two functions is equal to the sum of the integrals of the individual functions.

Step 3 ：So, \(\int_{a}^{b} (f(x) + g(t)) d x = \int_{a}^{b} f(x) d x + \int_{a}^{b} g(t) d t\).

Step 4 ：Substitute the given values: \(\int_{a}^{b} (f(x) + g(t)) d x = 6 + 4\).

Step 5 ：\(\int_{a}^{b} (f(x) + g(t)) d x = 10\).

Step 6 ：\(\boxed{10}\) is the final answer.