QString str = "an";
    ui->plainTextEdit->setPlainText("Hello world this\nan example to test");
    int begin = ui->plainTextEdit->toPlainText().indexOf(str); // get index of word start
    int end = begin + str.size(); // end of word
    qDebug() << begin << " " << end << endl;
    QTextCharFormat fmt;
    fmt.setBackground(Qt::yellow); // a char format 
//move on it and start highlight this word
    QTextCursor cursor(ui->plainTextEdit->document());
    cursor.setPosition(begin,QTextCursor::MoveAnchor);
    cursor.setPosition(end,QTextCursor::KeepAnchor);
    cursor.setCharFormat(fmt);

and this code to check the highlighted word if it's highlighted or not

    QString str = "an";
    int begin = ui->plainTextEdit->toPlainText().indexOf(str);
    int end = begin + str.size();

    QTextCursor cursor(ui->plainTextEdit->document());
    cursor.setPosition(begin,QTextCursor::MoveAnchor);
    cursor.setPosition(end,QTextCursor::KeepAnchor);
    QTextCharFormat fmt = cursor.charFormat();
    if (fmt.background() == Qt::yellow) {
        qDebug() << "YES highlighted";
    }
    else {
        qDebug() << "NO Not highlighted";
    }

it works fine
The problem is when I begin from early start if i make begin - 10 for example it ouput "yes highlighted" which is wrong so if I make begin = 0 and end stop at the position of the highlighted word it say YES if i increase the end it say no so it work from one side only
but it work when I extend the end if i make for example end + 10 it say no
why it make that and how to fix it
this the example of begin which have the problem

    QString str = "an";
    int begin = 0; // start from 0 which all not highlighted
    int end = ui->plainTextEdit->toPlainText().indexOf(str); + str.size(); and stop and end of the highlighted word

    QTextCursor cursor(ui->plainTextEdit->document());
    cursor.setPosition(begin,QTextCursor::MoveAnchor);
    cursor.setPosition(end,QTextCursor::KeepAnchor);
    QTextCharFormat fmt = cursor.charFormat();
    if (fmt.background() == Qt::yellow) {
        qDebug() << "YES"; // it ouput yes because just from the start to end contains a highlighted word
    }
    else {
        qDebug() << "NO";
    }

Thanks in advance