If `int_(0)^(100) f(x)dx=7,` then `sum_(r=1)^(100)int_(0)^(1)f(r-1+x)dx=`_________.

Explanation

To solve the problem, we need to evaluate the expression:

\[ \sum_{r=1}^{100} \int_{0}^{1} f(r-1+x) \, dx \]

### Step-by-Step Solution:

1. **Rewrite the Integral**:
We start with the expression:
\[ \sum_{r=1}^{100} \int_{0}^{1} f(r-1+x) \, dx \]

2. **Change of Variable**:
For each term in the summation, we can perform a change of variable. Let \( u = r - 1 + x \). Then, \( du = dx \), and when \( x = 0 \), \( u = r - 1 \) and when \( x = 1 \), \( u = r \). Thus, we have:
\[ \int_{0}^{1} f(r-1+x) \, dx = \int_{r-1}^{r} f(u) \, du \]

3. **Substituting Back into the Summation**:
Now substituting this back into the summation gives:
\[ \sum_{r=1}^{100} \int_{r-1}^{r} f(u) \, du \]

4. **Combining the Integrals**:
The summation can be combined into a single integral:
\[ \int_{0}^{100} f(u) \, du \]
This is because the limits of integration from \( r-1 \) to \( r \) for \( r = 1 \) to \( 100 \) cover the entire interval from \( 0 \) to \( 100 \).

5. **Using the Given Information**:
We are given that:
\[ \int_{0}^{100} f(x) \, dx = 7 \]

6. **Final Result**:
Therefore, we conclude that:
\[ \sum_{r=1}^{100} \int_{0}^{1} f(r-1+x) \, dx = \int_{0}^{100} f(x) \, dx = 7 \]

### Answer:
\[ \text{The required value is } 7. \]